Page 18 - Math Course 3 (Book 1)

Solving Linear Inequalities
Mo. 1

Lesson 3 Inequality Involving a Negative
Coefficient

Example
KEY CONCEPTS:
1. Solve linear inequalities involving more than
one operation. Solve 13 – 11d ≥ 79.
2. Solve linear inequalities involving the
Distributive Property. 13 – 11d ≥ 79 Original inequality

13 – 11d – 13 ≥ 79 – 13 Subtract 13 from each
side.
MO. 1 - L3a
–11d ≥ 66 Simplify.
Solving Linear Inequalities:
66
Multi-Step –11d ≤ –11 Divide each side by –11
change ≥ to ≤.
–11
d ≤ –6 Simplify.
Let’s Begin Answer The solution set is {d | d ≤ –6} .

Multi-Step Inequality Write and Solve an Inequality

Example Example

SCIENCE Define a variable, write an inequality, and solve the
problem below. Check your solution.
The inequality F > 212 represents the temperature
Four times a number plus twelve is less than a
in degrees Fahrenheit for which water is a gas number minus three.
9
represents
(steam). The inequality c + 32 > 212 a
5
the temperature in degrees Celsius for which water Four number
times a is less minus
is a gas. Find the temperatures in degrees Celsius number plus twelve than three.
for which water is a gas. 4n + 12 < n – 3
4n + 12 < n – 3 Original inequality
9 c + 32 > 212 Original inequality
5 4n + 12 – n < n – 3 – n Subtract n from each
9 c + 32– 32 > 212 – 32 Subtract 32 from each side.
5 side. 3n + 12 < –3 Simplify.

9 c > 180
5 Simplify. 3n + 12 – 12 < –3 – 12 Subtract 12 from each
5
5
5 9 c > 180 Multiply each side by side.
9 5 9 9 3n < –15 Simplify.
c > 100 Simplify.
3n < –15 Divide each side by 3.
3 3

n < –5 Simplify.
Answer Water is a gas for all temperature
greater than 100°C. 4n + 12 < n – 3;
Answer
The solution set is {n | n < –5}

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