Find the Roots (Zeros) |2x-9|=5

$| 2 x - 9 | = 5$

Step 1

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

$2 x - 9 = \pm 5$

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.

$2 x - 9 = 5$

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

Add $9$ to both sides of the equation.

$2 x = 5 + 9$

Add $5$ and $9$ .

$2 x = 14$

Divide each term in $2 x = 14$ by $2$ and simplify.

Divide each term in $2 x = 14$ by $2$ .

$\frac{2 x}{2} = \frac{14}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{14}{2}$

Divide $x$ by $1$ .

$x = \frac{14}{2}$

Simplify the right side.

Divide $14$ by $2$ .

$x = 7$

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

$2 x - 9 = - 5$

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

Add $9$ to both sides of the equation.

$2 x = - 5 + 9$

Add $- 5$ and $9$ .

$2 x = 4$

Divide each term in $2 x = 4$ by $2$ and simplify.

Divide each term in $2 x = 4$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $4$ by $2$ .

$x = 2$

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

$x = 7, 2$

Step 3

Find the Roots (Zeros) |2x-9|=5

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