This lesson is about inequalities and word problems with inequalities.

1. Skill 29 Inequalities
A mathematical sentence can have an “equals sign =“ or a sign that states an
Inequality . Both can and should be graphed on a number line. The “=“ graphs as a
single number or point. The inequalities are entire regions of the number line which
are shaded. Study the examples below. Use pages 148, 131a, 132a,b,c,d. in the book.
≤ means less than or equal to
Shade to the left of the number
with a filled in circle.
≥ means greater than or equal to
Shade to the right of the number
with a filled in circle.
< means less than but with
an open circle.
Means greater than but with
an open circle.

2. Solve an inequality the same way you would solve an equation. The
next several slides are examples of inequality problems.

3. Notice in this problem that the letter, y, is on the right. It is much easier to
graph the final solution if the letter (variable) is on the left. At the end of
the problem, rewrite the inequality with the letter on the left but keep the
pointed arrow toward the same number or letter.

5. The one big difference between solving equations and solving inequalities is concerns
multiplying or dividing by a negative. Read this.

6. Notice that the inequality sign is reversed at the moment we
divided by -3.

7. Notice that we don’t reverse the inequality sign
because we divided by positive 3.

9. Now some word problems.

11. Inequalities Translate the words to inequalities Use a letter (variable)
to represent the amount in each problem
1. Children must be at least 48 inches tall to ride the roller coaster.
2. A school bus can seat at most 48 students.
3. To avoid a ticket, your speed must be at most 55 mph.
4. The elevator can hold a maximum of 20 people.
5. You must be at least 16 to get a driver's license.
6. A crowd of at least 100 attended the parade.