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Question
Solve for x, the inequality given below.
`-5 ≤ (2 - 3x)/4 ≤ 9`
Solution
`-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`
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