What is the answer to |(5x+1)/(x-1)|=3 ?

The answer to |(5x+1)/(x-1)|=3 is x=-2,x= 1/4

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|(5x+1)/(x-1)|=3

\frac{5 x + 1}{x - 1} = 3

x = - 2, x = \frac{1}{4}

Solution steps

\frac{5 x + 1}{x - 1} = 3

Simplify

\frac{5 x + 1}{x - 1} : \frac{∣ 5 x + 1 ∣}{∣ x - 1 ∣}

\frac{∣ 5 x + 1 ∣}{∣ x - 1 ∣} = 3

Multiply both sides by

∣ x - 1 ∣

∣ 5 x + 1 ∣ = 3 ∣ x - 1 ∣

Solve

∣ 5 x + 1 ∣ = 3 ∣ x - 1 ∣ : x = - 2 or x = \frac{1}{4}

x = - 2, x = \frac{1}{4}

Verify Solutions

Find undefined (singularity) points:

x = 1

Combine undefined points with solutions:

x = - 2, x = \frac{1}{4}

\frac{\frac{3}{2}}{\frac{1}{2}}

x^{\frac{1}{2}} \cdot x^{\frac{3}{4}}

t^{2} - 4 t = 0

36 x^{2} - 96 x + 48 = 0

(3 x - 10)^{2} = 0

What is the answer to |(5x+1)/(x-1)|=3 ?
The answer to |(5x+1)/(x-1)|=3 is x=-2,x= 1/4
Solve for x: |(5x+1)/(x-1)|=3
The solution is x=-2,x= 1/4