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 7 – 2x:
7 – 2x = 0 → x =
(Subtracting by 7 on both the sides, then multiplying by -1 on both the sides and then dividing both the sides by 2)
7 – 2x < 0 → x >
(Subtracting by 7 on both the sides, then multiplying by -1 on both the sides and then dividing both the sides by 2)
7 – 2x > 0 → x <
(Subtracting by 7 on both the sides, then multiplying by -1 on both the sides and then dividing both the sides by 2)
Signs of x – 2:
x – 2 = 0 → x = 2 (Adding 2 on both the sides)
x – 2 < 0 → x < 2 (Adding 2 on both the sides)
x – 2 > 0 → x > 2 (Adding 2 on both the sides)
Zeroes of denominator:
x – 2 = 0 → x = 2
At x = 2, is not defined
Intervals satisfying the condition: < 0
x < 2 and
Therefore,