Title: Lesson 1–1
Author: Teri Willard
Last saved by: MHE

Lesson 1–5

Example 1      Solve an Inequality Using Addition or Subtraction
Solve 5w + 6 ≤ 4w – 2.5. Graph the solution set on a number line.
5w + 6 | ≤ | 4w – 2.5 | Original inequality
5w + 6 + (– 4w) | ≤ | 4w – 2.5 + (– 4w) | Add –4w to each side.
w + 6 | ≤ | –2.5 | Simplify.
w + 6 + (–6) | ≤ | –2.5 + (–6) | Add –6 to each side.
w | ≤ | –8.5 | Simplify.

Any real number less than or equal to –8.5 is a solution of this inequality.
The graph of the solution set is shown below.

CHECK	Substitute –8.5 for w in 5w + 6 ≤ 4w – 2.5. The two sides should be equal. Then substitute a number less than –8.5. The inequality should be true.

Example 2      Solve an Inequality Using Multiplication or Division
Solve  < 3.6. Graph the solution set on a number line.
< 3.6 | Original inequality
-5> -5(3.6) | Multiply each side by -5, reversing the inequality symbol.
z > -18 | Simplify.

A circle means that this point is not included in the solution set.

The solution set is {z | z > -18}.
The graph of the solution set is shown below.

Example 3      Solve a Multi–Step Inequality
Solve 14 – 2s ≥ . Graph the solution set on a number line.

14 – 2s ≥ | Original inequality
84 – 12s ≥ 3s + 9 | Multiply each side by 6.
84 – 15s ≥ 9 | Add –3s to each side.
–15s ≥ –75 | Add –84 to each side.
s ≤ 5 | Divide each side by –15, reversing the inequality symbol.
The solution set is (-, 5] and is graphed below.

Example 4      Write an Inequality
DELIVERIES  Roberto is delivering 5-gallon buckets of paint to a painting contractor. Each 5-gallon bucket weighs 55 pounds and Roberto weighs 188 pounds. If the maximum capacity of the tailgate lift on the truck is 1700 pounds, how many buckets of paint can Roberto take on each trip on the lift if he rides as well?

Explore	Let p = the number of buckets of paint Roberto can safely take on each trip. A maximum capacity of 1700 pounds means that the total weight must be less than or equal to 1700.

Plan	The total weight of the buckets of paint is 55p. Roberto’s weight plus the total weight of the paint must be less than or equal to 1700 pounds. Write an inequality.

Roberto's weight

plus

the weight 
of the paint

is less than 
or equal to

1700.

188 | + | 55p | ≤ | 1700

Solve | 188 + 55p ≤ 1700 | Original inequality
| 188 + 55p - 188 ≤ 1700 - 188 | Subtract 188 from each side.
| 55p ≤ 1512 | Simplify.
| | Divide each side by 55.
| p ≤ 27.49 | Simplify.

Check	Since he cannot take a fraction of a bucket, Roberto can take no more than 27 buckets per trip and still meet the safety requirements of the lift.