Solve each of the following in equations and represent the solution set on the number line.

.

Given:

.

Subtracting 2 from both the sides in the above equation

Signs of 3 – 2x:

3 – 2x = 0 → x =

(Subtracting by 3 on both the sides, then multiplying by -1 on both the sides and then dividing both the sides by 2)

3 – 2x < 0 → x >

(Subtracting by 3 on both the sides, then multiplying by -1 on both the sides and then dividing both the sides by 2)

3 – 2x > 0 → x <

(Subtracting by 3 on both the sides, then multiplying by -1 on both the sides and then dividing both the sides by 2)

Signs of x – 1:

x – 1 = 0 → x = 1 (Adding 1 on both the sides)

x – 1 < 0 → x < 1 (Adding 1 on both the sides)

x – 1 > 0 → x > 1 (Adding 1 on both the sides)

Zeroes of denominator:

x – 1 = 0 → x = 1

At x = 1, is not defined

Intervals satisfying the condition: ≤ 0

x < 1 and

Therefore,