Solve for x |2x-5|=4

$| 2 x - 5 | = 4$

Step 1

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

$2 x - 5 = \pm 4$

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.

$2 x - 5 = 4$

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

Add $5$ to both sides of the equation.

$2 x = 4 + 5$

Add $4$ and $5$ .

$2 x = 9$

Divide each term in $2 x = 9$ by $2$ and simplify.

Divide each term in $2 x = 9$ by $2$ .

$\frac{2 x}{2} = \frac{9}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{9}{2}$

Divide $x$ by $1$ .

$x = \frac{9}{2}$

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

$2 x - 5 = - 4$

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

Add $5$ to both sides of the equation.

$2 x = - 4 + 5$

Add $- 4$ 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 $1$ .

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

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

$x = \frac{9}{2}, \frac{1}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{9}{2}, \frac{1}{2}$

Decimal Form:

$x = 4.5, 0.5$

Mixed Number Form:

$x = 4 \frac{1}{2}, \frac{1}{2}$

Solve for x |2x-5|=4

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