What is the answer to |((2x-3))/((x-2))|=5 ?

The answer to |((2x-3))/((x-2))|=5 is x= 13/7 ,x= 7/3

Solve for x: |((2x-3))/((x-2))|=5

The solution is x= 13/7 ,x= 7/3

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\frac{( 2 x - 3 )}{( x - 2 )} = 5

x = \frac{13}{7}, x = \frac{7}{3}

Decimal Notation

x = 1.85714 \dots, x = 2.33333 \dots

Solution steps

\frac{( 2 x - 3 )}{( x - 2 )} = 5

Simplify

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

\frac{∣ 2 x - 3 ∣}{∣ x - 2 ∣} = 5

Multiply both sides by

∣ x - 2 ∣

∣ 2 x - 3 ∣ = 5 ∣ x - 2 ∣

Solve

∣ 2 x - 3 ∣ = 5 ∣ x - 2 ∣ : x = \frac{13}{7} or x = \frac{7}{3}

x = \frac{13}{7}, x = \frac{7}{3}

Verify Solutions

Find undefined (singularity) points:

x = 2

Combine undefined points with solutions:

x = \frac{13}{7}, x = \frac{7}{3}

\frac{\frac{12}{3}}{5.5} + \frac{\frac{17}{12}}{( 2.25 - x )} = \frac{11}{6}

2 (\frac{2}{3 \cdot y + 3}) + 2 (y + 5) = 130

\frac{( 25 x ^{3} )}{( ( x + 1 ) ^{2} )} = 64

(1) 2 \cdot (\frac{x + 1}{x})^{2} - 3 (\frac{x - 1}{x}) - 8 = 0

\frac{x}{3 \cdot x} = 9^{2}

What is the answer to |((2x-3))/((x-2))|=5 ?
The answer to |((2x-3))/((x-2))|=5 is x= 13/7 ,x= 7/3
Solve for x: |((2x-3))/((x-2))|=5
The solution is x= 13/7 ,x= 7/3