Solve for x |2x-7|+1=9

$| 2 x - 7 | + 1 = 9$

Step 1

Move all terms not containing $| 2 x - 7 |$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$| 2 x - 7 | = 9 - 1$

Subtract $1$ from $9$ .

$| 2 x - 7 | = 8$

Step 2

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

$2 x - 7 = \pm 8$

Step 3

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.

$2 x - 7 = 8$

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

Add $7$ to both sides of the equation.

$2 x = 8 + 7$

Add $8$ and $7$ .

$2 x = 15$

Divide each term in $2 x = 15$ by $2$ and simplify.

Divide each term in $2 x = 15$ by $2$ .

$\frac{2 x}{2} = \frac{15}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{15}{2}$

Divide $x$ by $1$ .

$x = \frac{15}{2}$

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

$2 x - 7 = - 8$

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

Add $7$ to both sides of the equation.

$2 x = - 8 + 7$

Add $- 8$ and $7$ .

$2 x = - 1$

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.

$x = \frac{15}{2}, - \frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{15}{2}, - \frac{1}{2}$

Decimal Form:

$x = 7.5, - 0.5$

Mixed Number Form:

$x = 7 \frac{1}{2}, - \frac{1}{2}$

Solve for x |2x-7|+1=9

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