Exercise 22 Page 73

We are told that at the start of the match the ball may not weight more than 16 ounces or less than 14 ounces . Let's break down what this means, write a compound inequality to represent the range, then graph it.

Graphing the Compound Inequality

The first thing to notice about the given information are the key words "not more than" and "not less than." These tell us that we have an "and" compound inequality, whose solution set is the overlap between the lesser value ( 14oz) and the greater value ( 16oz). Note, however, that before the soccer match began, the weight of the ball was increased by 1.5ounces before being approved for use. The expression w+1.5 represents the weight of the ball, which falls within the approved weight range.

Forming the Compound Inequality

Let's solve and rearrange the inequality in order to form compound inequality later.

w+1.5≥14

SubIneq

LHS-1.5≥RHS-1.5

w≥12.5

RearrangeEqn

Rearrange equation

12.5≤ w

Now consider the greater point, 16oz. Ball may not weight more than 16 ounces. w+1.5≤ 16 Let's solve for w.

w+1.5≤ 16

SubIneq

LHS-1.5≤RHS-1.5

w≤ 14.5

These two statements form an "and" compound inequality.

12.5≤ wand w≤ 14.5 ⇔ 12.5≤ w≤ 14.5

Note that the inequality is not strict, so on the graph we represent it with a closed points.