Question

Values for the area A of the rectangle shown are 12 ≤ A ≤ 36.

Answer 1

A compound inequality is used to combined multiple inequalities.

• The compound inequality is: $12 \le 6x \le 36$.
• The solution to the compound inequality is: $2 \le x \le 6$

We have:

$12 \le A \le 36$

$Length = 2x$

$Width = 3$

The area of the rectangle is:

$A = Length \times Width$

So, we have:

$A =2x \times 3$

$A = 6x$

Substitute 6x for A in $12 \le A \le 36$

$12 \le 6x \le 36$

Divide through by 6

$2 \le x \le 6$

Hence,

• The compound inequality is: $12 \le 6x \le 36$.
• The solution to the compound inequality is: $2 \le x \le 6$

Read more about compound inequalities at:

brainly.com/question/17957246