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

Given:

.

Signs of x – 7:

x – 7 = 0 x = 7(Adding 7 on both the sides)

x – 7 > 0 x > 7 (Adding 7 on both the sides)

x – 7 < 0 x < 7 (Adding 7 on both the sides)

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 at x = 2 will be undefined.

Intervals that satisfy the required condition: ≥ 0

x < 2 or x = 7 or x >7

Therefore,

x є (-∞, -2) υ [7, ∞)

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