Basic Math Examples

$| 8 s - 1 | + 2 = 13$

Step 1

Move all terms not containing $| 8 s - 1 |$ to the right side of the equation.

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Step 1.1

Subtract $2$ from both sides of the equation.

$| 8 s - 1 | = 13 - 2$

Step 1.2

Subtract $2$ from $13$ .

$| 8 s - 1 | = 11$

Step 2

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

$8 s - 1 = \pm 11$

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.

$8 s - 1 = 11$

Step 3.2

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

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Step 3.2.1

Add $1$ to both sides of the equation.

$8 s = 11 + 1$

Step 3.2.2

Add $11$ and $1$ .

$8 s = 12$

Step 3.3

Divide each term in $8 s = 12$ by $8$ and simplify.

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Step 3.3.1

Divide each term in $8 s = 12$ by $8$ .

$\frac{8 s}{8} = \frac{12}{8}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $8$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{8 s}{8} = \frac{12}{8}$

Step 3.3.2.1.2

Divide $s$ by $1$ .

$s = \frac{12}{8}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Cancel the common factor of $12$ and $8$ .

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Step 3.3.3.1.1

Factor $4$ out of $12$ .

$s = \frac{4 (3)}{8}$

Step 3.3.3.1.2

Cancel the common factors.

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Step 3.3.3.1.2.1

Factor $4$ out of $8$ .

$s = \frac{4 \cdot 3}{4 \cdot 2}$

Step 3.3.3.1.2.2

Cancel the common factor.

$s = \frac{4 \cdot 3}{4 \cdot 2}$

Step 3.3.3.1.2.3

Rewrite the expression.

$s = \frac{3}{2}$

Step 3.4

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

$8 s - 1 = - 11$

Step 3.5

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

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Step 3.5.1

Add $1$ to both sides of the equation.

$8 s = - 11 + 1$

Step 3.5.2

Add $- 11$ and $1$ .

$8 s = - 10$

Step 3.6

Divide each term in $8 s = - 10$ by $8$ and simplify.

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Step 3.6.1

Divide each term in $8 s = - 10$ by $8$ .

$\frac{8 s}{8} = \frac{- 10}{8}$

Step 3.6.2

Simplify the left side.

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Step 3.6.2.1

Cancel the common factor of $8$ .

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Step 3.6.2.1.1

Cancel the common factor.

$\frac{8 s}{8} = \frac{- 10}{8}$

Step 3.6.2.1.2

Divide $s$ by $1$ .

$s = \frac{- 10}{8}$

Step 3.6.3

Simplify the right side.

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Step 3.6.3.1

Cancel the common factor of $- 10$ and $8$ .

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Step 3.6.3.1.1

Factor $2$ out of $- 10$ .

$s = \frac{2 (- 5)}{8}$

Step 3.6.3.1.2

Cancel the common factors.

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Step 3.6.3.1.2.1

Factor $2$ out of $8$ .

$s = \frac{2 \cdot - 5}{2 \cdot 4}$

Step 3.6.3.1.2.2

Cancel the common factor.

$s = \frac{2 \cdot - 5}{2 \cdot 4}$

Step 3.6.3.1.2.3

Rewrite the expression.

$s = \frac{- 5}{4}$

Step 3.6.3.2

Move the negative in front of the fraction.

$s = - \frac{5}{4}$

Step 3.7

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

$s = \frac{3}{2}, - \frac{5}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$s = \frac{3}{2}, - \frac{5}{4}$

Decimal Form:

$s = 1.5, - 1.25$

Mixed Number Form:

$s = 1 \frac{1}{2}, - 1 \frac{1}{4}$