# Study Guide Section 5.2

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```Name __________________________________
Date ___________________
LESSON 5.2
Study Guide
For use with the lesson “Solve Inequalities Using Multiplication and Division”
GOAL
Solve inequalities using multiplication and division.
Multiplication Property of Inequality
Multiplying each side of an inequality by a positive number produces an equivalent
inequality.
Multiplying each side of an inequality by a negative number and reversing the direction
of the inequality symbol produces an equivalent inequality.
EXAMPLE 1
Solve an inequality using multiplication
Solve the inequality. Graph your solution.
x
a.
>3
7
x
b.
≤5
2
Solution
a.
x
>3
7
x
7 >73
7
x > 21
Write original inequality.
Multiply each side by 7.
Simplify.
The solutions are all real numbers greater than 21. Check by substituting a number
greater than 21 in the original inequality.
b.
x
≤5
2
x
–2 
≥ –2  5
2
x ≥ –10
Write original inequality.
Multiply each side by –2. Reverse inequality symbol.
Simplify.
The solutions are all real numbers greater than or equal to –10. Check by substituting a
number greater than or equal to –10 in the original inequality.
Exercises for example 1
Solve the inequality. Graph the solution
m
1.
< –3
4
n
2.
≤4
6
3. p > –8
1.2
Name __________________________________
Date ___________________
LESSON 5.2
Study Guide continued
EXAMPLE 2
Solve an inequality using division
Solve 6x > –36.
Solution
6x > –36
6 x 36
>
6
6
x > –6
Write original inequality.
Divide each side by 6.
Simplify.
Exercises for Example 2
Solve the inequality.
4. –3x ≤ 9
5. 18 ≥ 9x
6. 6x < 12
EXAMPLE 3
Solve a real-world problem_________________________________________
A library has \$180 to buy new books. The books cost \$9 each. Write and solve an
inequality to find the possible number of books that can be bought for the library.
Solution
The total cost of the books can be at most the amount of money available. Write a verbal
model for the situation. Then write an inequality.
Books· Cost per book
b 
9
≤ 180
≤ 180
b ≤ 20
The library can afford to buy at most 20 books.
Exercises for Example 3
7. In Example 3, suppose the library has \$120 to spend and that books cost \$8 each.
Write and solve an inequality to find the possible number of books the library can
8. Three sisters want to buy a PDA for their father for Father’s Day. The least
expensive PDA in the store is \$360. Write and solve an inequality to find the least
amount of money each girl would have to contribute, if each contributes an equal
amount.
Lesson 5.2
Study Guide
1. m < –12;
2. n 24;
3. p < 9.6;
4.
5.
6.
7.
8.
x  –3
2x
x<2
b  15
s  120
```