Solve for x |2x-5|=6

$| 2 x - 5 | = 6$

Step 1

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

$2 x - 5 = \pm 6$

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.

$2 x - 5 = 6$

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

Add $5$ to both sides of the equation.

$2 x = 6 + 5$

Add $6$ and $5$ .

$2 x = 11$

Divide each term in $2 x = 11$ by $2$ and simplify.

Divide each term in $2 x = 11$ by $2$ .

$\frac{2 x}{2} = \frac{11}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{11}{2}$

Divide $x$ by $1$ .

$x = \frac{11}{2}$

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

$2 x - 5 = - 6$

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

Add $5$ to both sides of the equation.

$2 x = - 6 + 5$

Add $- 6$ and $5$ .

$2 x = - 1$

Divide each term in $2 x = - 1$ by $2$ and simplify.

Divide each term in $2 x = - 1$ by $2$ .

$\frac{2 x}{2} = \frac{- 1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 1}{2}$

Divide $x$ by $1$ .

$x = \frac{- 1}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{2}$

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

$x = \frac{11}{2}, - \frac{1}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{11}{2}, - \frac{1}{2}$

Decimal Form:

$x = 5.5, - 0.5$

Mixed Number Form:

$x = 5 \frac{1}{2}, - \frac{1}{2}$

Solve for x |2x-5|=6

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