Solve each of the following in equations and represent the solution se

1.	Solve each of the following in equations and represent the solution set on the number line.\(\cfrac{{\text{x}}-7}{{\text{x}}-2}\)\(\ge\) 0, X ∈ R
Answer» Given: \(\cfrac{{\text{x}}-7}{{\text{x}}-2}\)\(\ge\) 0, X ∈ R \(\cfrac{{\text{x}}-7}{{\text{x}}-2}\)\(\ge\) 0 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 \(\cfrac{{\text{x}}-7}{{\text{x}}-2}\) will be undefined intervals that satisfy the required condition: \(\ge\) 0 x < 2 or x = 7 or x >7 Therefore, x є (-∞, -2) υ [7, ∞)

Solve each of the following in equations and represent the solution set on the number line.\(\cfrac{{\text{x}}-7}{{\text{x}}-2}\)\(\ge\) 0, X ∈ R

Answer»

Given:

\(\cfrac{{\text{x}}-7}{{\text{x}}-2}\)\(\ge\) 0, X ∈ R

\(\cfrac{{\text{x}}-7}{{\text{x}}-2}\)\(\ge\) 0

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 \(\cfrac{{\text{x}}-7}{{\text{x}}-2}\) will be undefined

intervals that satisfy the required condition: \(\ge\) 0

x < 2 or x = 7 or x >7

Therefore,

x є (-∞, -2) υ [7, ∞)