Chapter 1: Expressions, Equations & Inequalities Section 5: Solving Inequalities
Name ______Date ______Period ______
Solving Inequalities
*If you are absent the day we complete this handout together in class it is your responsibility to fill it in; please borrow from a friend to get the notes you missed!
· Inequality Symbols
o < is “less than”
o > is “greater than”
o ≤ is “less than or equal to”
o ≥ is “greater than or equal to”
· Simple Inequalities
o Only one inequality symbol
o Solve like a regular equation
§ Special Case: When you multiply or divide by a negative number, the inequality switches. Greater than becomes less than and vice versa. But, remember this only happens when multiply or dividing by a negative number!
o Once the inequality have been solved for the variable, the solution can be graphed on a number line.
§ Open circle is for < or >
§ Closed circle is for ≤ or ≥
o Let’s try a few: Solve if necessary and then graph on a number line.
1. x < 7
2. 0 ≤ y
3. 2p - 2 > 10
4. h + 1 ≤ -3
5. -33 < n
6. 5y – 8 < 12
7. 2(x + 2) - 2 ≤ 6x – 2
8. 4x + 5 > 25
· Compound Inequalities
o Joined by “and” or “or”; two inequality symbols
o “AND”
§ Solve as one big equation
§ Will look like a dumb bell on a graph
§ Ex. -2 ≤ 3h -8 ≤ 10
§ Ex. -16 ≤ 3x – 4 ≤ 2
§ Ex. 3 < 2x + 11 ≤ 17
o “OR”
§ Solve each equation separately
§ Will have arrows pointing to both ends of the number line
§ Ex. 2x + 3 < 5 or 4x -7 > 9
§ Ex. 3a + 1 < -2 or 3a + 1 > 7
§ Ex. X – 7 ≥ 2 or x – 7 < -2