Question

COMPOUND INEQUALITIES Please answer question 26

Answer 1

Answer: 6 ≤ x ≤ 8

Explanation:

We will use the formula for the area of a right triangle to solve this compound inequality to solve for A.

Given:

`\displaystyle A = (bh)/(2)`

Substitute known values:

`\displaystyle A = (3x)/(2)`

Now, we know that the area must be greater than or equal to 9 and less than or equal to 12. We will solve for x by substituting our expression for the area into the given compound inequality.

9 ≤ A ≤ 12

9 ≤
`(3x)/(2)` ≤ 12

18 ≤ 3x ≤ 24

6 ≤ x ≤ 8