What is the answer to (|x-2|)/(x+1)=5 ?

The answer to (|x-2|)/(x+1)=5 is x=-1/2

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(|x-2|)/(x+1)=5

\frac{∣ x - 2 ∣}{x + 1} = 5

x = - \frac{1}{2}

Solution steps

\frac{∣ x - 2 ∣}{x + 1} = 5

Multiply both sides by

x + 1

∣ x - 2 ∣ = 5 (x + 1)

Solve

∣ x - 2 ∣ = 5 (x + 1) : x = - \frac{1}{2}

x = - \frac{1}{2}

Verify Solutions

Find undefined (singularity) points:

x = - 1

Combine undefined points with solutions:

x = - \frac{1}{2}

x^{- 1} = - 3

\frac{3}{x - 2} + 3 = \frac{4 x}{x - 2}

y^{- 3} = 64

0 = \frac{x + 2}{x - 6}

- \frac{2 x + 2}{x + 3} = 6