Question

For the following inequation, graph the solution set on the real number line:

–1 < 3 – 2x ≤ 7

Answer 1

Given,

–1 < 3 – 2x ≤ 7

Solving L.H.S. of the equation,

⇒ -–1 < 3 – 2x

⇒ –1 – 3 < –2x

⇒ –4 < –2x

Dividing both sides by –2 we get,

⇒ 2 > x (As sign reverses on dividing by negative no.)

⇒ x < 2 .....(i)

Solving R.H.S. of the equation,

⇒ 3 – 2x ≤ 7

⇒ 3 – 7 ≤ 2x

⇒ –4 ≤ 2x

Dividing both sides by 2 we get,

⇒ –2 ≤ x

⇒ x ≥ –2 ....(ii)

From (i) and (ii) we get,

–2 ≤ x < 2

∴ Solution set = {x : x ∈ R and –2 ≤ x < 2}

Solution on the number line is: