x ∈ {real numbers} and -1 < 3 - 2x ≤ 7, evaluate x and represent it on a number line.

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 :