Algebra Examples

$\frac{1}{2} (s - 12) = \frac{1}{4} (s + 16)$

Step 1

Simplify $\frac{1}{2} \cdot (s - 12)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{2} \cdot (s - 12) = \frac{1}{4} \cdot (s + 16)$

Step 1.2

Simplify by adding zeros.

$\frac{1}{2} \cdot (s - 12) = \frac{1}{4} \cdot (s + 16)$

Step 1.3

Apply the distributive property.

$\frac{1}{2} s + \frac{1}{2} \cdot - 12 = \frac{1}{4} \cdot (s + 16)$

Step 1.4

Combine $\frac{1}{2}$ and $s$ .

$\frac{s}{2} + \frac{1}{2} \cdot - 12 = \frac{1}{4} \cdot (s + 16)$

Step 1.5

Cancel the common factor of $2$ .

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Step 1.5.1

Factor $2$ out of $- 12$ .

$\frac{s}{2} + \frac{1}{2} \cdot (2 (- 6)) = \frac{1}{4} \cdot (s + 16)$

Step 1.5.2

Cancel the common factor.

$\frac{s}{2} + \frac{1}{2} \cdot (2 \cdot - 6) = \frac{1}{4} \cdot (s + 16)$

Step 1.5.3

Rewrite the expression.

$\frac{s}{2} - 6 = \frac{1}{4} \cdot (s + 16)$

Step 2

Simplify $\frac{1}{4} \cdot (s + 16)$ .

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Step 2.1

Apply the distributive property.

$\frac{s}{2} - 6 = \frac{1}{4} s + \frac{1}{4} \cdot 16$

Step 2.2

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

$\frac{s}{2} - 6 = \frac{s}{4} + \frac{1}{4} \cdot 16$

Step 2.3

Cancel the common factor of $4$ .

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Step 2.3.1

Factor $4$ out of $16$ .

$\frac{s}{2} - 6 = \frac{s}{4} + \frac{1}{4} \cdot (4 (4))$

Step 2.3.2

Cancel the common factor.

$\frac{s}{2} - 6 = \frac{s}{4} + \frac{1}{4} \cdot (4 \cdot 4)$

Step 2.3.3

Rewrite the expression.

$\frac{s}{2} - 6 = \frac{s}{4} + 4$

Step 3

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

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Step 3.1

Subtract $\frac{s}{4}$ from both sides of the equation.

$\frac{s}{2} - 6 - \frac{s}{4} = 4$

Step 3.2

To write $\frac{s}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{s}{2} \cdot \frac{2}{2} - \frac{s}{4} - 6 = 4$

Step 3.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{s}{2}$ by $\frac{2}{2}$ .

$\frac{s \cdot 2}{2 \cdot 2} - \frac{s}{4} - 6 = 4$

Step 3.3.2

Multiply $2$ by $2$ .

$\frac{s \cdot 2}{4} - \frac{s}{4} - 6 = 4$

Step 3.4

Combine the numerators over the common denominator.

$\frac{s \cdot 2 - s}{4} - 6 = 4$

Step 3.5

Subtract $s$ from $s \cdot 2$ .

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Step 3.5.1

Reorder $s$ and $2$ .

$\frac{2 \cdot s - s}{4} - 6 = 4$

Step 3.5.2

Subtract $s$ from $2 \cdot s$ .

$\frac{s}{4} - 6 = 4$

Step 4

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

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Step 4.1

Add $6$ to both sides of the equation.

$\frac{s}{4} = 4 + 6$

Step 4.2

Add $4$ and $6$ .

$\frac{s}{4} = 10$

Step 5

Multiply both sides of the equation by $4$ .

$4 \frac{s}{4} = 4 \cdot 10$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Cancel the common factor of $4$ .

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Step 6.1.1.1

Cancel the common factor.

$4 \frac{s}{4} = 4 \cdot 10$

Step 6.1.1.2

Rewrite the expression.

$s = 4 \cdot 10$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $4$ by $10$ .

$s = 40$