Solve for x |2x-1|+8=x

$| 2 x - 1 | + 8 = x$

Subtract $8$ from both sides of the equation.

$| 2 x - 1 | = x - 8$

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$2 x - 1 = \pm (x - 8)$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$2 x - 1 = x - 8$

Move all terms containing $x$ to the left side of the equation.

Subtract $x$ from both sides of the equation.

$2 x - 1 - x = - 8$

Subtract $x$ from $2 x$ .

$x - 1 = - 8$

Move all terms not containing $x$ to the right side of the equation.

Add $1$ to both sides of the equation.

$x = - 8 + 1$

Add $- 8$ and $1$ .

$x = - 7$

Next, use the negative value of the $\pm$ to find the second solution.

$2 x - 1 = - (x - 8)$

Simplify $- (x - 8)$ .

Rewrite.

$2 x - 1 = 0 + 0 - (x - 8)$

Simplify by adding zeros.

$2 x - 1 = - (x - 8)$

Apply the distributive property.

$2 x - 1 = - x - - 8$

Multiply $- 1$ by $- 8$ .

$2 x - 1 = - x + 8$

Move all terms containing $x$ to the left side of the equation.

Add $x$ to both sides of the equation.

$2 x - 1 + x = 8$

Add $2 x$ and $x$ .

$3 x - 1 = 8$

Move all terms not containing $x$ to the right side of the equation.

Add $1$ to both sides of the equation.

$3 x = 8 + 1$

Add $8$ and $1$ .

$3 x = 9$

Divide each term in $3 x = 9$ by $3$ and simplify.

Divide each term in $3 x = 9$ by $3$ .

$\frac{3 x}{3} = \frac{9}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{9}{3}$

Divide $x$ by $1$ .

$x = \frac{9}{3}$

Simplify the right side.

Divide $9$ by $3$ .

$x = 3$

The complete solution is the result of both the positive and negative portions of the solution.

$x = - 7, 3$

Exclude the solutions that do not make $| 2 x - 1 | + 8 = x$ true.

$No solution$

Solve for x |2x-1|+8=x

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