Solve for x, the inequalities in

Question:
Solve for x, the inequalities in

$-5 \leq \frac{2-3 \mathrm{x}}{4} \leq 9$

Solution:

According to the question,

$-5 \leq \frac{2-3 x}{4} \leq 9$

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