Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

Add $3$ to both sides of the equation.

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

Step 2.2.2

Add $1$ and $3$ .

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

Step 2.3

Multiply both sides of the equation by $2$ .

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

Step 2.4

Simplify both sides of the equation.

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Step 2.4.1

Simplify the left side.

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Step 2.4.1.1

Cancel the common factor of $2$ .

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Step 2.4.1.1.1

Cancel the common factor.

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

Step 2.4.1.1.2

Rewrite the expression.

$x = 2 \cdot 4$

Step 2.4.2

Simplify the right side.

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Step 2.4.2.1

Multiply $2$ by $4$ .

$x = 8$

Step 2.5

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

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

Step 2.6

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

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Step 2.6.1

Add $3$ to both sides of the equation.

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

Step 2.6.2

Add $- 1$ and $3$ .

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

Step 2.7

Multiply both sides of the equation by $2$ .

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

Step 2.8

Simplify both sides of the equation.

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Step 2.8.1

Simplify the left side.

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Step 2.8.1.1

Cancel the common factor of $2$ .

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Step 2.8.1.1.1

Cancel the common factor.

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

Step 2.8.1.1.2

Rewrite the expression.

$x = 2 \cdot 2$

Step 2.8.2

Simplify the right side.

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Step 2.8.2.1

Multiply $2$ by $2$ .

$x = 4$

Step 2.9

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

$x = 8, 4$