Basic Math Examples

$| s + 12 | = 3 s$

Step 1

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

$s + 12 = \pm 3 s$

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.

$s + 12 = 3 s$

Step 2.2

Move all terms containing $s$ to the left side of the equation.

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Step 2.2.1

Subtract $3 s$ from both sides of the equation.

$s + 12 - 3 s = 0$

Step 2.2.2

Subtract $3 s$ from $s$ .

$- 2 s + 12 = 0$

Step 2.3

Subtract $12$ from both sides of the equation.

$- 2 s = - 12$

Step 2.4

Divide each term in $- 2 s = - 12$ by $- 2$ and simplify.

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Step 2.4.1

Divide each term in $- 2 s = - 12$ by $- 2$ .

$\frac{- 2 s}{- 2} = \frac{- 12}{- 2}$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $- 2$ .

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Step 2.4.2.1.1

Cancel the common factor.

$\frac{- 2 s}{- 2} = \frac{- 12}{- 2}$

Step 2.4.2.1.2

Divide $s$ by $1$ .

$s = \frac{- 12}{- 2}$

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Divide $- 12$ by $- 2$ .

$s = 6$

Step 2.5

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

$s + 12 = - 3 s$

Step 2.6

Move all terms containing $s$ to the left side of the equation.

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Step 2.6.1

Add $3 s$ to both sides of the equation.

$s + 12 + 3 s = 0$

Step 2.6.2

Add $s$ and $3 s$ .

$4 s + 12 = 0$

Step 2.7

Subtract $12$ from both sides of the equation.

$4 s = - 12$

Step 2.8

Divide each term in $4 s = - 12$ by $4$ and simplify.

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Step 2.8.1

Divide each term in $4 s = - 12$ by $4$ .

$\frac{4 s}{4} = \frac{- 12}{4}$

Step 2.8.2

Simplify the left side.

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Step 2.8.2.1

Cancel the common factor of $4$ .

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Step 2.8.2.1.1

Cancel the common factor.

$\frac{4 s}{4} = \frac{- 12}{4}$

Step 2.8.2.1.2

Divide $s$ by $1$ .

$s = \frac{- 12}{4}$

Step 2.8.3

Simplify the right side.

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Step 2.8.3.1

Divide $- 12$ by $4$ .

$s = - 3$

Step 2.9

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

$s = 6, - 3$

Step 3

Exclude the solutions that do not make $| s + 12 | = 3 s$ true.

$s = 6$