Solve for x |x+6|=2x-1

$| x + 6 | = 2 x - 1$

Step 1

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

$x + 6 = \pm (2 x - 1)$

Step 2

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.

$x + 6 = 2 x - 1$

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

Subtract $2 x$ from both sides of the equation.

$x + 6 - 2 x = - 1$

Subtract $2 x$ from $x$ .

$- x + 6 = - 1$

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

Subtract $6$ from both sides of the equation.

$- x = - 1 - 6$

Subtract $6$ from $- 1$ .

$- x = - 7$

Divide each term in $- x = - 7$ by $- 1$ and simplify.

Divide each term in $- x = - 7$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 7}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 7}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 7}{- 1}$

Simplify the right side.

Divide $- 7$ by $- 1$ .

$x = 7$

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

$x + 6 = - (2 x - 1)$

Simplify $- (2 x - 1)$ .

Rewrite.

$x + 6 = 0 + 0 - (2 x - 1)$

Simplify by adding zeros.

$x + 6 = - (2 x - 1)$

Apply the distributive property.

$x + 6 = - (2 x) - - 1$

Multiply.

Multiply $2$ by $- 1$ .

$x + 6 = - 2 x - - 1$

Multiply $- 1$ by $- 1$ .

$x + 6 = - 2 x + 1$

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

Add $2 x$ to both sides of the equation.

$x + 6 + 2 x = 1$

Add $x$ and $2 x$ .

$3 x + 6 = 1$

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

Subtract $6$ from both sides of the equation.

$3 x = 1 - 6$

Subtract $6$ from $1$ .

$3 x = - 5$

Divide each term in $3 x = - 5$ by $3$ and simplify.

Divide each term in $3 x = - 5$ by $3$ .

$\frac{3 x}{3} = \frac{- 5}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 5}{3}$

Divide $x$ by $1$ .

$x = \frac{- 5}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{5}{3}$

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

$x = 7, - \frac{5}{3}$

Step 3

Exclude the solutions that do not make $| x + 6 | = 2 x - 1$ true.

$x = 7$

Solve for x |x+6|=2x-1

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