Pre-Algebra Examples

$| x + 3 | - 4 = 6$

Step 1

Move all terms not containing $| x + 3 |$ to the right side of the equation.

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Step 1.1

Add $4$ to both sides of the equation.

$| x + 3 | = 6 + 4$

Step 1.2

Add $6$ and $4$ .

$| x + 3 | = 10$

Step 2

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

$x + 3 = \pm 10$

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.

$x + 3 = 10$

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 $3$ from both sides of the equation.

$x = 10 - 3$

Step 3.2.2

Subtract $3$ from $10$ .

$x = 7$

Step 3.3

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

$x + 3 = - 10$

Step 3.4

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

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Step 3.4.1

Subtract $3$ from both sides of the equation.

$x = - 10 - 3$

Step 3.4.2

Subtract $3$ from $- 10$ .

$x = - 13$

Step 3.5

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

$x = 7, - 13$