5-1 One/Two Step Inequalities / 2 days
5-2 Multi-Step Inequalities / 2 days
5-3 Compound Inequalities / 3 days
5.1 - 5.3 Quiz / 1 day
5-4 Absolute Value Inequalities / 4 days
5-5 Graphing Two Variable Inequalities / 3 days
Test Review / 1 day
Test / 1 day
Cumulative Review / 1 day
Total days in Unit 5 –Inequalities = 18 days
Review Question
What four things make up an equation? Numbers, variables, operations, and equal sign
Discussion
What makes an equation, an equation? Equal sign
What makes an inequality, an inequality? Inequality
greater than
≥ greater than or equal to
less than
≤ less than or equal to
What is the answer to x + 4 = 9? There is one solution. It is 5. Look at the solution on a number line.
What is the answer to x + 4 > 9? Anything bigger than 5. There is an infinite amount of solutions. Look at the solution on a number line.
As far as we know, an equation has one solution. An inequality has an infinite number of solutions.
SWBATsolve a one/two-step inequality
Definitions
greater than
≥ greater than or equal to
less than
≤ less than or equal to
Example 1: x + 4 > 9 x + 4 > 9
Is it solved? No, the variable is not by itself. - 4 - 4
What is with the variable? Plus 4 x > 5
How do you get rid of plus four? Subtract 4
Keep the two sides of the inequality “balanced”
by subtracting by 4 on both sides.
Graph.
Why isn’t the 5 coloredin? It is not included in the solution set.
The final solution is x 5.
What does the solution mean? Any number greater than five will work.
Example 2: 2x + 5 92x + 5 9
Is it solved? No - 5 - 5
What is with the variable? Plus 5, times 2 2x4
What do we get rid of first? Why? Plus 5 2 2
How do we get rid of plus 5? Minus 5 x 2
How do we get rid of times 2? Divide by 2
Graph.
Why is the 2 coloredin? It is included in the solution set.
The final solution is x 2.
What does the solution mean? Any number less than or equal to two will work.
Discussion
6 = 6
What happens when you multiply/divide both sides of the equation by 3? Stays equal
What happens when you multiply/divide both sides of the equation by -3? Stays equal
6 > 3
What happens when you multiply/divide both sides of the equation by 3? Inequality stays true
What happens when you multiply/divide both sides of the equation by -3?Inequality isn’t true
So, if we multiply or divide by a negative number, we must flip the inequality.
Example 3: -4y – 8 > 8-4y – 8 > 8
Is it solved? No + 8 + 8
What is with the variable? Minus 8, times -4 -4y16
What do we get rid of first? Why? Minus 8 -4 -4
How do we get rid of minus 8? Plus 8 y < -4
How do we get rid of times -4? Divide by -4
Why do we flip the inequality? Divided by a negative
The final solution is y < -4.
What does the solution mean? Any number less than negative four will work.
Graph.
Example 4:
Is it solved? No - 2 - 2
What is with the variable? Plus 2, divided by 3
What do we get rid of first? Why? Plus 2 x < -18
How do we get rid of plus 2? Minus 2
How do we get rid of divided by 3? Multiply by 3
Why don’t we flip the inequality? We are not multiplying by a negative.
The final solution is x -18.
What does the solution mean? Any number less than -18 will work.
Graph.
You Try!
Solve. Then graph your solution.
1. 2x – 6 8 x < 7
2. -3x – 7 > 14 x < -7
3. x > -10
4. x > 6
5. 2x – 4 > -12 x > -4
6. x -12
What did we learn today?
Solve each inequality. Then graph your solution.
1. 3x 12 x > 42. x < 20
3. -5z 20z -44. x > -12
5. y – 6 7 y 136. z + 1 8z < 7
7. 5x + 3 23 x > 48. 3x – 14 4 x 6
9. -3y – 5 19 y < -810. 5x + 6 -29 x -7
11. 8 – 5y -37 y < 912. 18 – 4y 42 y -6
13. .4y – 3 -1 y < 514. 3.2x + 2.6 -23 x >-8
15. x > 1216. x -6
17. x > 918. -5y + 10 -15 y 5
19. x >2020. 5 + 4y 25 y >5
Review Question
When do we flip the inequality symbol? When we multiply/divide by a negative number
Discussion
We wrote equations in Unit 2 like: Two more than twice a number is equal to twenty.
2n + 2 = 20
Today, we will write inequalities. We write them the same as equations.
What do we need to have an inequality? Variable, operations, numbers, inequality
Steps to writing an inequality:
1. Define a variable
2. Look for keywords
Add – increase, more than, etc
Subtract – decrease, less than, etc
Multiply – times, of, etc
Divide – quotient, half, etc
3. Look for inequality words: greater than, less than, etc.
SWBATwrite and solve a one/two-step inequality
Example 1: Write and solve the inequality. Then graph.
Seven times a number plus four is greater than twenty-five.
7n + 4 25
– 4 – 4
7n21
7 7
n > 3
Example 2: Write and solve the inequality. Then graph.
Twenty less than twice an integer is less than or equal to ten.
2i – 20 10
+20 + 20
2i30
2 2
i 15
Example 3: Write and solve the inequality. Then graph.
The quotient of x and negative two minus five is greater than three.
+ 5 + 5
x < -16
What did we learn today?
Solve each inequality. Then graph your solution.
1. 4x + 3 < 15x < 32. -3x + 8 8 x 0
3. x -244. 8 + 2y > 20 y6
Write and solve the inequality. Then graph.
5. A number decreased by 5 is less than 22. n 27
6. Seven times a number is greater than 28. n > 4
7. The quotient of a number and 5 increased by 2 is greater than -10. n > -60
8. Four times a number increased by six is less than or equal to eighteen. n 3
9. The opposite of 2x plus nine is less than negative nine. x 9
10. Three times a number increased by five is greater than 20. n 5
11. Four less than three times a number is greater than or equal to 20.n 8
12. The quotient of a number and -4, less 8, is less than -2.x -24
13. Twenty more than three times a number is at least -4.n -8
14. Eight less than ten times a number is greater than 82.n 9
15. The difference between twice a number and 9 is at most 17.n 13
Review Question
When do you flip the inequality sign?When you multiply/divide by a negative number
Discussion
We solved more complicated equations in Unit 2 like this: 3(4x + 2) = 10x – 20.
Today, we will do the same with inequalities.
SWBATsolve a multi-step inequality
Example 1: Solve. Then graph your solution.
Collect all of the variables on one side then get the variable by itself by performing opposite operations.
8x + 10 > 6x – 20
- 6x - 6x
2x + 10 > -20
- 10 - 10
2x-30
2 2
x > -15
Why didn’t we flip the inequality? Didn’t divide by a negative
What does the solution mean? Any number greater than negative fifteen will work.
Example 2: Solve. Then graph your solution.
Distribute. Combine like terms. Collect all of the variables on one side then get the variable by itself by performing opposite operations.
3(x + 6) + 2x < 5x + 12
3x + 18 + 2x < 5x + 12
5x + 18 < 5x + 12
- 5x - 5x
18 < 12
When is 18 < 12? Never; therefore the answer is empty set.
What does that answer mean? No number will work.
How could it be All Reals? 18 < 12; All numbers would work.
Graph.
Example 3: Solve. Then graph your solution.
Distribute. Combine like terms. Collect all of the variables on one side then get the variable by itself by performing opposite operations.
8x – (2x + 4) 4x + 10
8x – 2x – 4 4x + 10
6x – 4 4x + 10
- 4x - 4x
2x – 4 10
+ 4 + 4
2x14
2 2
x 7
You Try!
Solve. Then graph your solution.
1. 4x + 12 > 2x + 24 x > 62. 15x 5(2x + 10) x 10
3. 2x – (x – 5) 2x + 17 x -124. 3(2x + 2) > 6x – 4 All Reals
5. 8x + 4 2(x + 6) + 6x Empty Set6. x > 3
What did we learn today?
Solve. Then graph the solution.
1. 4x + 10 2x + 20 x 52. 6x + 4 3x + 13 x 3
3. 3x – 5 + 7x <-25 x < -24. 3x + 10 < -11 x < -7
5. 3 – 4x 10x + 10 x -1/26. 2(3y + 1) < 6 + 6y All Reals
7. 4(x – 2) > 4x Empty Set8. 6(x + 2) – 4 -10 x -3
9. 4(2y – 1) > -10(y – 5) y >310. 3(1 + y) 3y + 3 All Reals
11. 2(x – 3) + 5 > 3(x – 1) x <212. 6x + 7 8x – 13 x 10
13. 8y + 9 > 7y + 6 y-314. 2x + 8 > 20 x >6
15. 5.3 + 2.8x > 4.9x + 1.1 x <216. -5x + 15 10 x 1
17. 5x – 9 -3x + 7 x >218. -3(2n – 5) 4n + 8 n7/10
19. 2(2x + 3) + 4x > 7x + 4 x <-220. x -26
Review Question
Let’s take a look at problem #10 on last night’s homework. When we solve it we get 0 0. When is this true?
It says “When is 0 less than or equal to 0.” The key word is “or.” It only has to be one or the other (less than OR equal to). Zero is always less than OR equal to zero. This will help us during the next section.
Discussion
We wrote equations in Unit 2 like: Two more than twice a number is equal to twenty less than 3n.
2n + 2 = 3n – 20. Today, we will write inequalities. We write them the same as equations.
SWBATwrite and solve a multi-step inequality
Example 1: Write and solve the inequality. Then graph your solution.
Eight less than four times a number is at least six more than twice the number.
What does at least mean? Let’s see…
I want to get at least an 80 on my next test. What does that mean? I want to get an 80 or higher. So .
Collect all of the variables on one side then get the variable by itself by performing opposite operations.
4n – 8 2n + 6
- 2n - 2n
2n – 8 6
+ 8 + 8
2n14
2 2
n 7
Example 2: Write and solve the inequality. Then graph your solution.
Three times the quantity of 2n + 9 is less than 11 decreased by twice a number.
Distribute. Collect all of the variables on one side then get the variable by itself by performing opposite operations.
3(2n + 9) < 11 – 2n
6n + 27 < 11 – 2n
+ 2n + 2n
8n + 27 < 11
- 27 - 27
8n-16
8 8
n < -2
Why didn’t we flip the inequality? Didn’t divide by a negative
What did we learn today?
Solve. Then graph the solution.
1. 8x + 2 2x + 20 x > 32. 6x + 4 + 4x 24 x 2
3. 2x – 8 7x – 38 x > 64. -4x + 10 < -18 x >7
5. 5 – 8x 10x + 23 x -16. -4(3y + 1) < 6 – 12y All Reals
7. -(x + 5) > -x Empty Set8. 2(x + 2) – 4 -8 x -4
9. 4(3y – 1) > -10(y – 5) y27/1110. -3x + 8 + 5x > 8 x 0
Write an inequality. Then solve.
11. Twice a number decreased by 5 is less than 21. n < 13
12. Seven times a number increased by 10 is greater than 31. n > 3
13. An integer increased by 10 is at least 20. i 10
14. Five less than negative four times a number is at most 19. n -6
15. Four times a number plus ten is less than or equal to two times a number decreased by twenty.
n -15
16. Negative 8x plus five is greater than seven less than 4x. x 1
17. Four times the quantity of 3n + 5 is less than or equal to 10n – 8. n -14
18. The quotient of a number and 5 increased by 2 is greater than -10. n > -60
Review Question
When do you flip the inequality sign?When you multiply/divide by a negative number
Discussion
Today’s lesson involves understanding the words and, and or.
So let’s try a real life example first.
I’m in my house and at school. When? Never
I’m in my house or at school. When? When I’m at one place or the other.
SWBAT solve a compound inequality.
Definitions
And – both things must be true
Or – at least one thing must be true
Example 1: x < 3 and x > -5
(Use dry erase boards as a visual. Have two students hold dry erase boards in the front of the class. One student will put a ‘3’ on their board with an arrow pointing left. The other student will have a
‘-5’ on their board with an arrow pointing right. Have the students visualize where both things are happening.)
What does ‘and’ mean? Both things must be true.
When are both things true? -5 < x < 3
Example 2: x < 3 or x > -5
What does ‘or’ mean? At least one thing must be true.
When is at least one thing true? All of the time. All Reals.
Example 3: x > 3 and x 7
What does ‘and’ mean? Both things must be true.
When are both things true? x 7
Example 4: x 3 or x 7
What does ‘or’ mean? At least one thing must be true.
When is at least one thing true? x 3
You Try!
Solve.
1. x > 4 and x < -2 Empty Set
2. x > 4 or x < -2 x > 4 or x < -2
3. x 3 and x > 4 x > 4
4. x 3 or x > 4 x 3
What did we learn today?
Solve each compound inequality.
1. x 3 and x < 12 2. x -5 or x > -3
3. x < -1 and x < -10 4. x > 5 or x < -8
5. x > -5 and x < -11 6. x > -5 or x < 5
7. x > -8 and x 8 8. x 5 and x < 8
9. x < -3 and x < -6 10. x > 3 or x > -5
Review Question
What is the difference between and and or?
And – both things must be true
Or – at least one thing must be true
Let’s make sure we know what we are doing:
x > -2 and x < 5
What does ‘and’ mean? Both things must be true.
When are both things true? -2 < x < 5
Discussion
Today, we are going to combine the idea of and and or with our solving skills.
2x + 5 > 11 or 3x – 5 < 10
We will solve each inequality first. Then figure out the correct solution set by using our summary skills from yesterday.
SWBATsolve a compound inequality
Definitions
And – both things must be true
Or – at least one thing must be true
Example 1: -3x + 8 > -1 or 3(2x + 4) < 24
- 8 - 8 6x + 12 < 24
3x-9 - 12 - 12
3 3 6x12
x > -3 6 6
x 2
What does ‘or’ mean? At least one thing must be true.
When is at least one thing true? Always, All Reals
Example 2: 3 < 2x + 7 and 3x + 2x + 6 21
- 7 - 7 5x + 6 21
-42x - 6 - 6
2 2 5x15
-2 < x 5 5
x 3
What does ‘and’ mean? Both things must be true.
When are both things true? -2 < x 3
Example 3: 5x + 7 > 32 and 2x – 5 5
- 7 - 7 + 5 + 5
5x25 2x10
5 5 2 2
x > 5 x 5
What does ‘and’ mean? Both things must be true.
When are both things true? Never; Empty Set
You Try!
Solve.
1. 3x + 5 < -7 or -4x + 8 20 x < -4 or x -3
2. -1 < x + 3 < 5 -4 < x < 2
3. 2(x – 4) < 3x + 6 and x – 8 < 4 – x -14 < x < 6
4. 2x – 8 + 3x 7or3(2x + 4) 30 All Reals
What if problem #4 was ‘and’ not ‘or’? The answer would be just ‘3’.
What did we learn today?
Solve each compound inequality.
1. x > 5 and x < 6 2. x > -4 or x > -2
3. x < 4 and x > 6 4. x 0 or x < 1
5. x > -3 and x > 5 6. x > 6 or x < -2
7. x + 8 3 and x + 9 -4-13 x -58. x – 10 < -21 or x + 3 < 2x < -1
9. 4 < 2y – 2 < 103 < y < 610. 8 > 5 – 3x and 5 – 3x > -13-1 < x < 6
11. -1 + x 3 or -x -4 All Reals12. 3n + 11 13 or -3n -12n 4
13. 3y + 12 6 + y 3y – 18Empty Set14. 0.5b > -6 or 3b + 16 < -8 + b All Reals except -12
15. 3(2x – 4) > 6 or 3x + 4x + 5 > 33 x > 3 16. 5x + 5 < 3x + 11 and 4x + 5 > -11 -4 < x < 3
Write an appropriate inequality. Then solve.
17. The sum of 3 times a number and 4 is between -8 and 10.-8 < 3n + 4 < 10; -4 < n < 2
18. One half a number is greater than 0 and less than or equal to 1. 1 > 1/2n > 0; 0 n 2
Review Question
What is the difference between and and or?
And – both things must be true
Or – at least one thing must be true
Discussion
Let’s make sure we know what we are doing by going over some homework problems.
How do you get better at something? Practice
Therefore, we are going to practice solving compound inequalities today.
We are going to have many days like this during the school year. In order for you to be successful, you need to take advantage of the time and ask your classmates and teachers’ questions.
SWBATsolve a compound inequality
Example 1: 3x + 8 8 or 3x + 14 > 2 – x
- 8 - 8 + x + x
3x0 4x + 14 > 2
3 3 - 14 - 14
x 0 4x-12
4 4
x > -3
What does ‘or’ mean? At least one thing must be true.
When is at least one thing true? x > -3
Example 2: 5x + 7 < 27 and -3x – 5 > -8
- 7 - 7 + 5 + 5
5x20 -3x-3
5 5 -3 -3
x < 4 x < 1
What does ‘and’ mean? Both things must be true.
When are both things true? x < 1
Solve each compound inequality.
1. x > 3 and x < 8 2. x > 5 or x > -2
3. x < -3 and x > 5 4. x > -2 or x < 1
5. x > 3 and x > 5 6. x > 3 or x < -3
7. x > 5 or x < 5 8. x > -3 and x -3
9. x + 3 < 7 or x – 6 > 8 x < 4 or x > 1410. 2x + 6 < 12 and -4x + 10 < -22 Empty Set
11. 3x + 2 > 5 or 6 + 3x < 2x + 712. or
All Reals except 1x < -11 or x > 4
13. -3x + 5 < 20 or 14. 2(3x – 3) > 5 and 2x + 4x – 5 > 2x + 15
x > -5 x > 5
15. 3(x + 1) + 11 < -2(x + 13) and 3x + 2(4x + 2) < 2(6x + 1)
Empty Set
What did we learn today?
Review Question
What is the difference between and and or?
And – both things must be true
Or – at least one thing must be true
Discussion
What does absolute value mean? The distance something is from zero.
Notice that distance is always positive. For example, if you travel to Florida it is not a negative distance because you went south. You can see this on a map. Going south or west on a map does not represent a negative distance. Also, if you run around the track the “other way” you are not running a negative distance. So: | 3 | = 3 because 3’s distance from ‘0’ is ‘3’. So: | -3 | = 3because -3’s distance from ‘0’ is ‘3’.
SWBATsolve an inequality with an absolute value
Example 1: This is a difficult topic so try some easy ones first:
a. |x| = 3 When is x’s distance from zero equal to ‘3’? When ‘x’ is 3 or -3
b. |x| > 3 When is x’s distance from zero greater than ‘3’? When x > 3 or x < -3
c. |x| < 3When is x’s distance from zero less than ‘3’? When x 3 and x -3; -3 < x < 3
Example 2:
a. |x| = 7.2 When is x’s distance from zero equal to ‘7.2’? When ‘x’ is 7.2 or -7.2
b. |x| > 7.2 When is x’s distance from zero greater than ‘7.2’? When x > 7.2 or x < 7.2
c. |x| < 7.2 When is x’s distance from zero less than ‘7.2’? When x < -7.2 and x > 7.2; -7.2 < x < 7.2
You Try!
1. |x| = 2 x = 2 or -2
2. |x| 6 -6 x 6
3. |x| > 4.2 x 4.2 or x -4.2
4. |x| 7 x 7 or x -7
5. |x|1 -1 x 1
What did we learn today?
Solve each inequality.
1. | x | = 5
2. | x | < 3
3. | x | > 1
4. | x | 6
5. | x | > 10
6. | x | > 2
7. | x | < 9
8. | x | 10
9. | x | 4.5
10. | x | >
Review Question
What does absolute value mean? The distance something is from zero.
Notice that distance is always positive.
Discussion
You always want to make absolute statements. So:
Is a > problem always ‘or’? No.
Is a < problem always ‘and’? No.
Why not? Can anyone think of a counterexample?
SWBATsolve an inequality with an absolute value
Example 1:
a. |x| > -5When is x’s distance from zero greater than ‘-5’?
Always. > problems are not always ‘or’
b. |x| < -5When is x’s distance from zero less than ‘-5’?
Never. < problems are not always ‘and’
Example 2:
a. |x| > 0When is x’s distance from zero greater than ‘0’?
When x > 0 or x < 0; Everything except ‘0’
b. |x| 0When is x’s distance from zero less than ‘0’?
Never, distance can’t be negative
c. |x| 0When is x’s distance from zero less than or equal to ‘0’?
When x = 0; Think of not going on vacation. How far did you travel? 0 miles
d. |x| 0When is x’s distance from zero greater than or equal to ‘0’?
Always. Distance is always positive.
* > problems are not always ‘or’; < problems are not always ‘and’
You Try!
1. |x| =4 x =4 or -4
2. |x| 8 -8 x 8
3. |x| > -2 All Reals
4. |x| 0 Empty Set
5. |x| 5.2 x < -5.2 or x > 5.2
6. |x| -6 Empty Set
What did we learn today?
Solve each inequality.
1. | x | =7
2. | x | < 6
3. | x | > -1
4. | x | 3
5. | x | > 0
6. | x | > 4.2
7. | x | < -9
8. | x | 1
9. | x | 2.5
10. | x | >
Review Question
Let’s make sure we understand some easy ones first:
|x| = 2 x = 2 or -2
|x| > 2 x > 2 or x < -2
|x| < 2 -2 < x < 2
Discussion
What would | pen | > 3 mean?
The distance that the pen is from zero is the following: pen > 3 or pen < -3.
SWBATsolve an inequality with an absolute value
Example 1: |x – 3| = 5
What does this question mean? When is the distance of ‘x – 3’ from zero equal to five.
How can this happen? When x – 3 = 5 or x – 3 = -5
x – 3 = 5 or x – 3 = -5
+ 3 + 3 + 3 + 3
x = 8 or x = -2
Example 2: |2x + 3| < 11
What does this question mean? When is the distance of ‘2x + 3’ from zero less than eleven.
How can this happen? When 2x + 3 11and 2x + 3 > -11
2x + 3 < 11 and 2x + 3 > -11
- 3 - 3 - 3 - 3
2x8 2x-14
2 2 2 2
x < 4 and x > -7
-7 < x < 4
Example 3: |2x + 3| > 11
What does this question mean? When is the distance of ‘2x + 3’ from zero greater than eleven.
How can this happen? When 2x + 3 11or 2x + 3 < -11
2x + 3 > 11 or 2x + 3 < -11
- 3 - 3 - 3 - 3
2x8 2x-14
2 2 2 2
x > 4 or x < -7
You Try!
1. |5x – 5 | = 15 4, -22. |2x + 4| 6 -5 < x < 1
3. |2x + 4| > 10x > 3 or x < -74. |4x + 2| < -7 Empty Set
5. |-x + 2| < 4-2 < x < 66. |6x + 2| > -6All Reals
What did we learn today?
Solve.
1. | x | = 7
2. | x | < 2
3. | x | 5
4. | x | > -3
5. | x | < -2
6. | x – 5 | = 8
7. | x + 9 | =2
8. | 2x – 3 | =17
9. | 5x – 8 | =12
10. | x – 2 | 5
11. | x + 8 | < 2
12. | x + 3 | 1
13. | x – 6 | 3
14. | 3x + 2 | -7
15. | 2x + 4 | 8
16. | 2x + 1 | 9
17. | 6x + 8 | -1
18. |-x + 3 | 1
Review Question
What would | pen | < 3 mean?
The distance that the pen is from zero is the following: -3 < pen < 3.
Discussion
Why can’t we always assume that a “>” problem is an “or?”
Can you give an example of a “>” problem that isn’t an “or?”
|x + 3| > -4; All Real Numbers
How do you get better at something? Practice
Therefore, we are going to practice solving absolute value inequalities today. We are going to have many days like this during the school year. In order for you to be successful, you need to take advantage of the time and ask your classmates and teachers’ questions.
SWBATsolve an inequality with an absolute value
You Try!
1. |5x + 10 | = 5 -1, -32. |2x + 5| < 9 -7< x < 2
3. |x + 8| 1 x -7 or x -94. |2x – 3| > -2 All Reals
5. |-x + 5| < 4 1 < x < 96. |2x – 4| 0 x = 2
What did we learn today?
Solve each inequality.
1. | x | = 52. | x | < 6
3. | x | 14. | x | > -5
5. | x | < -86. |x| 0
7. | x – 4 | = 8-4, 128. | x + 8 | =2 -10, -6
9. | 2x – 4 | =12 8, -410. | 5x – 5 | =20 5, -3
11. | x – 5 | 5 0 x 1012. | x + 5 | < 2 -7 < x < -3
13. | 2x + 4 | 8 x 2 or x -614. | -2x – 6 | 3 x -4.5 or x -1.5
15. | 2x + 2 | -7 All Reals16. | 6x + 8 | -1 Empty Set
Review Question
How would you graph y = 2x + 3? Start at (0, 3), up 2 over 1
Discussion
How would you graph x > 3?
Notice we shade to the right. How do we know how to do this? We just know right.
But what we are really doing is checking to see which numbers “work”. If 4, 5, 6, etc. work, then we know to shade to the right. We know that if 2, 1, 0, etc. don’t work, then we need to shade on the other side.
We are going to do a similar thing to determine which side of the line needs to be shaded today. We are going to test points on one side of the line and see if they work.
SWBATgraph an inequality with two variables
Example 1: Graph: y 2x + 3
First let’s graph the line like it was an equation: start at (0, 3), then go up 2 over 1.
Now we need to determine which side of the line needs to be shaded. We are going to try the point (0, 0). We choose this point because it is easy. When we put (0, 0) into the inequality, we get 0 2(0) + 3, which results in 0 < 3. Notice that this inequality is true. Therefore, the point (0, 0) works. This means that any other point on this side of the line will work. Therefore, we need to shade everything on this side of the line.