Solve for x 5+|1-x/2|=8

$5 + | 1 - \frac{x}{2} | = 8$

Step 1

Move all terms not containing $| 1 - \frac{x}{2} |$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

$| 1 - \frac{x}{2} | = 8 - 5$

Subtract $5$ from $8$ .

$| 1 - \frac{x}{2} | = 3$

Step 2

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

$1 - \frac{x}{2} = \pm 3$

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.

$1 - \frac{x}{2} = 3$

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

Subtract $1$ from both sides of the equation.

$- \frac{x}{2} = 3 - 1$

Subtract $1$ from $3$ .

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

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{x}{2}) = - 2 \cdot 2$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 2 (- \frac{x}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{x}{2}$ into the numerator.

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

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- x}{2} = - 2 \cdot 2$

Cancel the common factor.

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

Rewrite the expression.

$- - x = - 2 \cdot 2$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 2 \cdot 2$

Multiply $x$ by $1$ .

$x = - 2 \cdot 2$

Simplify the right side.

Multiply $- 2$ by $2$ .

$x = - 4$

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

$1 - \frac{x}{2} = - 3$

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

Subtract $1$ from both sides of the equation.

$- \frac{x}{2} = - 3 - 1$

Subtract $1$ from $- 3$ .

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

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{x}{2}) = - 2 \cdot - 4$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 2 (- \frac{x}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{x}{2}$ into the numerator.

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

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- x}{2} = - 2 \cdot - 4$

Cancel the common factor.

$2 \cdot - 1 \frac{- x}{2} = - 2 \cdot - 4$

Rewrite the expression.

$- - x = - 2 \cdot - 4$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 2 \cdot - 4$

Multiply $x$ by $1$ .

$x = - 2 \cdot - 4$

Simplify the right side.

Multiply $- 2$ by $- 4$ .

$x = 8$

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

$x = - 4, 8$

Solve for x 5+|1-x/2|=8

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