Solve for x |2x+5|=7

$| 2 x + 5 | = 7$

Step 1

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

$2 x + 5 = \pm 7$

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.

$2 x + 5 = 7$

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

Subtract $5$ from both sides of the equation.

$2 x = 7 - 5$

Subtract $5$ from $7$ .

$2 x = 2$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $2$ by $2$ .

$x = 1$

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

$2 x + 5 = - 7$

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

Subtract $5$ from both sides of the equation.

$2 x = - 7 - 5$

Subtract $5$ from $- 7$ .

$2 x = - 12$

Divide each term in $2 x = - 12$ by $2$ and simplify.

Divide each term in $2 x = - 12$ by $2$ .

$\frac{2 x}{2} = \frac{- 12}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 12}{2}$

Divide $x$ by $1$ .

$x = \frac{- 12}{2}$

Simplify the right side.

Divide $- 12$ by $2$ .

$x = - 6$

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

$x = 1, - 6$

Solve for x |2x+5|=7

Related Questions

Support LCMGCF.com by disabling your adblocker.