Intermediate Algebra (11th edition)

Using the Multiplication Property of Inequality

Solve each inequality, and graph the solution set.

(a)

Divide each side by 5. Since do not reverse the direction of the inequal-

ity symbol.

Divide by 5.

Check that the solution set is the interval 1 - q, - 64 ,graphed in FIGURE 11.

x...- 6

5 x

5

...

- 30

5

5 x...- 30

5 >0,

5 x...- 30

EXAMPLE 3

94 CHAPTER 2 Linear Equations, Inequalities, and Applications

NOW TRY
EXERCISE 3
Solve each inequality and
graph the solution set.

(a)

(b) - 20 x7- 60

8 xÚ- 40

NOW TRY ANSWERS

3. (a)

(b) 1 - q, 3 2

3 - 5, q 2

–6 –5 –4 –3 –2

–101234

–14 –12 –10 –8 –6 –4 –2 0 2

FIGURE 11

(b)

Divide each side by Since reverse the direction of the inequality

symbol.

Divide by

Reverse the direction of the symbol.

xÚ- 8

- 4 x

- 4

Ú

32

- 4

- 4 x... 32

- 4.  4 <0,

- 4 x... 32

Reverse the

inequality symbol

when dividing by a

negativenumber.

Check the solution set. FIGURE 12shows the graph of the solution set, 3 - 8, q 2.

–9 –8 –7 –6 –5 –4 –3 –2 –1 0 1

FIGURE 12 NOW TRY

CAUTION Reverse the direction of the inequality symbol when multiplying or

dividing each side of an inequality by a negative number.

Multiplication Property of Inequality

For all real numbers A, B, and C, with

(a)the inequalities

and are equivalent if ;

(b) the inequalities

and are equivalent if.

That is, each side of an inequality may be multiplied (or divided) by a positive

number without changing the direction of the inequality symbol. Multiplying

(or dividing) by a negative number requires that we reverse the inequality

symbol.

ABC C< 0