Question

Solve for x, the inequality given below.

`-5 ≤ (2 - 3x)/4 ≤ 9`

Answer 1

`-5 ≤ (2 - 3x)/4 ≤ 9`

Multiplying each term by 4, we get

⇒ –20 ≤ 2 – 3x ≤ 36

Adding –2 each term, we get

⇒ –22 ≤ –3x ≤ 34

Dividing each term by 3, we get

⇒ `-22/3` ≤ –x ≤ `34/3`

We know that,

Multiplication by –1 inverts the inequality.

So, multiplying each term by –1, we get

⇒ `(-34)/3` ≤ x ≤ `22/3`