Algebra Examples

$| 4 - \frac{x}{2} | - 3 = 0$

Step 1

Add $3$ to both sides of the equation.

$| 4 - \frac{x}{2} | = 3$

Step 2

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

$4 - \frac{x}{2} = \pm 3$

Step 3

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

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Step 3.1

First, use the positive value of the $\pm$ to find the first solution.

$4 - \frac{x}{2} = 3$

Step 3.2

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

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Step 3.2.1

Subtract $4$ from both sides of the equation.

$- \frac{x}{2} = 3 - 4$

Step 3.2.2

Subtract $4$ from $3$ .

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

Step 3.3

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

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

Step 3.4

Simplify both sides of the equation.

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Step 3.4.1

Simplify the left side.

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Step 3.4.1.1

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

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Step 3.4.1.1.1

Cancel the common factor of $2$ .

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Step 3.4.1.1.1.1

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

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

Step 3.4.1.1.1.2

Factor $2$ out of $- 2$ .

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

Step 3.4.1.1.1.3

Cancel the common factor.

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

Step 3.4.1.1.1.4

Rewrite the expression.

$- - x = - 2 \cdot - 1$

Step 3.4.1.1.2

Multiply.

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Step 3.4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 2 \cdot - 1$

Step 3.4.1.1.2.2

Multiply $x$ by $1$ .

$x = - 2 \cdot - 1$

Step 3.4.2

Simplify the right side.

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Step 3.4.2.1

Multiply $- 2$ by $- 1$ .

$x = 2$

Step 3.5

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

$4 - \frac{x}{2} = - 3$

Step 3.6

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

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Step 3.6.1

Subtract $4$ from both sides of the equation.

$- \frac{x}{2} = - 3 - 4$

Step 3.6.2

Subtract $4$ from $- 3$ .

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

Step 3.7

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

$- 2 (- \frac{x}{2}) = - 2 \cdot - 7$

Step 3.8

Simplify both sides of the equation.

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Step 3.8.1

Simplify the left side.

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Step 3.8.1.1

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

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Step 3.8.1.1.1

Cancel the common factor of $2$ .

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Step 3.8.1.1.1.1

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

$- 2 \frac{- x}{2} = - 2 \cdot - 7$

Step 3.8.1.1.1.2

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- x}{2} = - 2 \cdot - 7$

Step 3.8.1.1.1.3

Cancel the common factor.

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

Step 3.8.1.1.1.4

Rewrite the expression.

$- - x = - 2 \cdot - 7$

Step 3.8.1.1.2

Multiply.

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Step 3.8.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 2 \cdot - 7$

Step 3.8.1.1.2.2

Multiply $x$ by $1$ .

$x = - 2 \cdot - 7$

Step 3.8.2

Simplify the right side.

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Step 3.8.2.1

Multiply $- 2$ by $- 7$ .

$x = 14$

Step 3.9

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

$x = 2, 14$