Algebra Examples

$| x + 3 | = 2 a + 3$

Step 1

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

$x + 3 = \pm (2 a + 3)$

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.

$x + 3 = 2 a + 3$

Step 2.2

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

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Step 2.2.1

Subtract $3$ from both sides of the equation.

$x = 2 a + 3 - 3$

Step 2.2.2

Combine the opposite terms in $2 a + 3 - 3$ .

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Step 2.2.2.1

Subtract $3$ from $3$ .

$x = 2 a + 0$

Step 2.2.2.2

Add $2 a$ and $0$ .

$x = 2 a$

Step 2.3

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

$x + 3 = - (2 a + 3)$

Step 2.4

Simplify $- (2 a + 3)$ .

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Step 2.4.1

Rewrite.

$x + 3 = 0 + 0 - (2 a + 3)$

Step 2.4.2

Simplify by adding zeros.

$x + 3 = - (2 a + 3)$

Step 2.4.3

Apply the distributive property.

$x + 3 = - (2 a) - 1 \cdot 3$

Step 2.4.4

Multiply.

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Step 2.4.4.1

Multiply $2$ by $- 1$ .

$x + 3 = - 2 a - 1 \cdot 3$

Step 2.4.4.2

Multiply $- 1$ by $3$ .

$x + 3 = - 2 a - 3$

Step 2.5

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

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Step 2.5.1

Subtract $3$ from both sides of the equation.

$x = - 2 a - 3 - 3$

Step 2.5.2

Subtract $3$ from $- 3$ .

$x = - 2 a - 6$

Step 2.6

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

$x = 2 a$

$x = - 2 a - 6$

$x = 2 a$

$x = - 2 a - 6$