Algebra Examples

$| x - 4 | = 7$

Step 1

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

$x - 4 = \pm 7$

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.

$x - 4 = 7$

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 $4$ to both sides of the equation.

$x = 7 + 4$

Step 2.2.2

Add $7$ and $4$ .

$x = 11$

Step 2.3

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

$x - 4 = - 7$

Step 2.4

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

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Step 2.4.1

Add $4$ to both sides of the equation.

$x = - 7 + 4$

Step 2.4.2

Add $- 7$ and $4$ .

$x = - 3$

Step 2.5

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

$x = 11, - 3$