Question

Phyllis solved the compound inequality 16 ≤ 2(3x – 1) < 28. She began by first breaking the inequality into two separate inequalities, then she correctly solved each for x.

Which graph represents her solution?

Answer 1

Explanation:

i) given equation is 16 ≤ 2(3x - 1) < 28

ii) separating the above into two equations we get

2(3x - 1) ≥ 16
`\Rightarrow` 3x - 1 ≥ 8
`\Rightarrow` 3x ≥ 9
`\Rightarrow` x ≥ 3

and

2(3x - 1) < 28
`\Rightarrow` 3x - 1 < 14
`\Rightarrow` 3x < 15
`\Rightarrow` x < 5

The graph representing Phyllis solution is given as graph attached.