Algebra Examples

$3 = - 2 | \frac{1}{4} s - 5 | + 3$

Step 1

Rewrite the equation as $- 2 | \frac{1}{4} s - 5 | + 3 = 3$ .

$- 2 | \frac{1}{4} s - 5 | + 3 = 3$

Step 2

Move all terms not containing $| \frac{1}{4} s - 5 |$ to the right side of the equation.

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Step 2.1

Subtract $3$ from both sides of the equation.

$- 2 | \frac{1}{4} s - 5 | = 3 - 3$

Step 2.2

Subtract $3$ from $3$ .

$- 2 | \frac{1}{4} s - 5 | = 0$

Step 3

Divide each term in $- 2 | \frac{1}{4} s - 5 | = 0$ by $- 2$ and simplify.

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Step 3.1

Divide each term in $- 2 | \frac{1}{4} s - 5 | = 0$ by $- 2$ .

$\frac{- 2 | \frac{1}{4} s - 5 |}{- 2} = \frac{0}{- 2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 2 | \frac{1}{4} s - 5 |}{- 2} = \frac{0}{- 2}$

Step 3.2.1.2

Divide $| \frac{1}{4} s - 5 |$ by $1$ .

$| \frac{1}{4} s - 5 | = \frac{0}{- 2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $0$ by $- 2$ .

$| \frac{1}{4} s - 5 | = 0$

Step 4

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

$\frac{1}{4} s - 5 = \pm 0$

Step 5

Plus or minus $0$ is $0$ .

$\frac{1}{4} s - 5 = 0$

Step 6

Combine $\frac{1}{4}$ and $s$ .

$\frac{s}{4} - 5 = 0$

Step 7

Add $5$ to both sides of the equation.

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

Step 8

Multiply both sides of the equation by $4$ .

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

Step 9

Simplify both sides of the equation.

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Step 9.1

Simplify the left side.

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Step 9.1.1

Cancel the common factor of $4$ .

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Step 9.1.1.1

Cancel the common factor.

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

Step 9.1.1.2

Rewrite the expression.

$s = 4 \cdot 5$

Step 9.2

Simplify the right side.

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Step 9.2.1

Multiply $4$ by $5$ .

$s = 20$

Step 10

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

$\frac{1}{4} s - 5 = \pm 0$

Step 11

Plus or minus $0$ is $0$ .

$\frac{1}{4} s - 5 = 0$

Step 12

Combine $\frac{1}{4}$ and $s$ .

$\frac{s}{4} - 5 = 0$

Step 13

Add $5$ to both sides of the equation.

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

Step 14

Multiply both sides of the equation by $4$ .

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

Step 15

Simplify both sides of the equation.

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Step 15.1

Simplify the left side.

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Step 15.1.1

Cancel the common factor of $4$ .

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Step 15.1.1.1

Cancel the common factor.

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

Step 15.1.1.2

Rewrite the expression.

$s = 4 \cdot 5$

Step 15.2

Simplify the right side.

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Step 15.2.1

Multiply $4$ by $5$ .

$s = 20$