Exercise 4 Page 68

Inequalities can be solved in the same way as equations, by performing inverse operations on both sides until the variable is isolated. The only difference is that when you divide or multiply by a negative number, you must reverse the inequality sign.

-18>1.5q

NumberToDenomMultFrac

a = 2 * a/2

-18>3/2q

MultIneq

LHS* 2/3 > RHS * 2/3

(-18)*2/3>3/2q*2/3

MultFracByInverse

a/b* b/a=1

(-18)*2/3>q

MoveLeftFacToNum

a*b/c= a* b/c

(- 18)* 2/3>q

MultNegPos

(- a)b = - ab

- 36/3>q

CalcQuot

Calculate quotient

- 12>q

RearrangeIneq

Rearrange inequality

q<-12

The above tells us that all values less than -12 will satisfy the inequality. Below we demonstrate the inequality by graphing the solution set on a number line. Notice that q cannot equal -12, which we show with an open circle on the number line.