Writing and Graphing Inequalities

Key Vocabulary: NOTES: Keep in mind that inequalities share a lot of similarities to equations. An inequality can be true, false or “open”. Putting variables in inequalities makes them “open”.

Inequality:An inequality is a mathematical sentence that shows relationships between two quantities that are not equivalent.

Algebraic Inequality:An inequality that contains at least ONE variable. To solve these, you want to isolate the variable on one side – just like solving an algebraic equation.

Solution Set:The set that contains ALL of the values found making a statement true. In an inequality you have a set of numbers that can work.

Part I: Inequality Key Words and Phrases

Symbol / Phrases / Symbol / Phrases
fewer than, less than, under / Above, more than, greater than, exceeds, over
≤ / There are at the most, less than or equal to, No more than / ≥ / There are at least, greater than or equal to, No less than

Part I Practice: Using the key words and phrases, write an inequality.

1. There are fewer than 25 students (s) in the class. / 2. Above 18 people (p) in the room had brown hair.
3. There are at least 15 dogs (d) in the park. / 4. No more than 50 people (p) were on the bus.
5. There are at most 31 days (d) in a month. / 6. There is more than $282 (d) in the bank
7. A bus can seat 48 students or fewer. / 8. There are over 20 species of crocodiles displayed
9. In many states, you have to be at least 16 years old to obtain a driver’s license. / 10. A light bulb more than 600 watts will not work in this fixture.
11. The Navy’s flying team, the Blue Angels, makes no fewer than 75 appearances each year. / 12. There must have been at least 200 students who attended the dance Saturday night.

Part II: Graphing SimpleInequalities:

  • An open circle (one not colored in) on the number line means the inequality will NOT include that number and the inequality sign must be > or <
  • A closed circle on the number line (a circle colored in) means the inequality DOES include that number and the inequality sign must be ≥ or ≤

Graph the following inequalities.

x < -2
/ g > 7
-3 ≥ y
/ m ≤ 0

Looking at the graphs, write an inequality.


Inequality: /
Inequality:

Inequality: /
Inequality:

Using the inequalities you wrote in Part I, graph each inequality.

1. There are fewer than 25 students (s) in the class.
/ 2. Above 18 people (p) in the room had brown hair.
3. There are at least 15 dogs (d) in the park.
/ 4. No more than 50 people (p) were on the bus.

5. There are at most 31 days (d) in a month.
/ 6. There is more than $282 (d) in the bank.

7. Bus Problem / 8. Crocodile Problem
9. Driver License Problem / 10. Light Bulb Problem