Question

Solve `-15 < (3(x-2))/5 <= 0,` x ∈ R and represent the solution on the number line.

Answer 1

`-15 < (3(x-2))/5 <= 0,` x ∈ R

Eliminate the denominator

Multiply all parts of the inequality by 5:

5(−15) < 3(x − 2) ≤ 5(0)

⇒ −75 < 3(x − 2) ≤ 0

Divide by 3

`(-75)/3 < x -2 <= 0/3`

⇒ −25 < x − 2 ≤ 0

−25 + 2 < x ≤ 0 + 2

⇒ −23 < x ≤ 2

x ∈ (−23, 2)