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

The answer to |x-2|= 1/(3x+2) is x=-(-2+sqrt(13))/3 ,x=(2+sqrt(13))/3 ,x=(2+sqrt(19))/3

Solve for x: |x-2|= 1/(3x+2)

The solution is x=-(-2+sqrt(13))/3 ,x=(2+sqrt(13))/3 ,x=(2+sqrt(19))/3

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∣ x - 2 ∣ = \frac{1}{3 x + 2}

x = - \frac{- 2 + 13}{3}, x = \frac{2 + 13}{3}, x = \frac{2 + 19}{3}

Decimal Notation

x = - 0.53518 \dots, x = 1.86851 \dots, x = 2.11963 \dots

Solution steps

∣ x - 2 ∣ = \frac{1}{3 x + 2}

Multiply both sides by

3 x + 2

∣ x - 2 ∣ (3 x + 2) = 1

Solve

∣ x - 2 ∣ (3 x + 2) = 1 : x = - \frac{- 2 + 13}{3} or x = \frac{2 + 13}{3} or x = \frac{2 + 19}{3}

x = - \frac{- 2 + 13}{3}, x = \frac{2 + 13}{3}, x = \frac{2 + 19}{3}

Verify Solutions

Find undefined (singularity) points:

x = - \frac{2}{3}

Combine undefined points with solutions:

x = - \frac{- 2 + 13}{3}, x = \frac{2 + 13}{3}, x = \frac{2 + 19}{3}

\frac{( 2 x - 2 )}{( x ^{2} - 2 x )} = 2.4

\frac{( x ^{2} + 4 x )}{3 + ( \frac{84}{x ^{2}} + 4 x )} = 11

\frac{x}{( x + 10 )} = 0.94

\frac{1}{3 x ^{2} ( x - 3 ) + x ^{2}} = - 9

\frac{d}{( x + 10 )} - \frac{d}{( x - 10 )} = 4

What is the answer to |x-2|= 1/(3x+2) ?
The answer to |x-2|= 1/(3x+2) is x=-(-2+sqrt(13))/3 ,x=(2+sqrt(13))/3 ,x=(2+sqrt(19))/3
Solve for x: |x-2|= 1/(3x+2)
The solution is x=-(-2+sqrt(13))/3 ,x=(2+sqrt(13))/3 ,x=(2+sqrt(19))/3