What is the answer to |(3-x)/(2+x)|=1 ?

The answer to |(3-x)/(2+x)|=1 is x= 1/2

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|(3-x)/(2+x)|=1

\frac{3 - x}{2 + x} = 1

x = \frac{1}{2}

Solution steps

\frac{3 - x}{2 + x} = 1

Simplify

\frac{3 - x}{2 + x} : \frac{∣ 3 - x ∣}{∣ 2 + x ∣}

\frac{∣ 3 - x ∣}{∣ 2 + x ∣} = 1

Multiply both sides by

∣ 2 + x ∣

∣ 3 - x ∣ = ∣ 2 + x ∣

Solve

∣ 3 - x ∣ = ∣ 2 + x ∣ : x = \frac{1}{2}

x = \frac{1}{2}

Verify Solutions

Find undefined (singularity) points:

x = - 2

Combine undefined points with solutions:

x = \frac{1}{2}

\frac{5}{3} = \frac{4}{y} - 1

2 = \frac{x + 7}{x - 10}

3 = - \frac{6}{d}

50 = \frac{1}{x}

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