Pre-Algebra Examples

$s + 2 \frac{1}{2} \cdot s + 20 = 62$

Step 1

Simplify the left side.

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Step 1.1

Simplify $s + 2 \frac{1}{2} \cdot s + 20$ .

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Step 1.1.1

Convert $2 \frac{1}{2}$ to an improper fraction.

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Step 1.1.1.1

A mixed number is an addition of its whole and fractional parts.

$s + (2 + \frac{1}{2}) \cdot s + 20 = 62$

Step 1.1.1.2

Add $2$ and $\frac{1}{2}$ .

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Step 1.1.1.2.1

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

$s + (2 \cdot \frac{2}{2} + \frac{1}{2}) \cdot s + 20 = 62$

Step 1.1.1.2.2

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

$s + (\frac{2 \cdot 2}{2} + \frac{1}{2}) \cdot s + 20 = 62$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$s + \frac{2 \cdot 2 + 1}{2} \cdot s + 20 = 62$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $2$ by $2$ .

$s + \frac{4 + 1}{2} \cdot s + 20 = 62$

Step 1.1.1.2.4.2

Add $4$ and $1$ .

$s + \frac{5}{2} \cdot s + 20 = 62$

Step 1.1.2

Combine $\frac{5}{2}$ and $s$ .

$s + \frac{5 s}{2} + 20 = 62$

Step 1.1.3

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

$s \cdot \frac{2}{2} + \frac{5 s}{2} + 20 = 62$

Step 1.1.4

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

$\frac{s \cdot 2}{2} + \frac{5 s}{2} + 20 = 62$

Step 1.1.5

Combine the numerators over the common denominator.

$\frac{s \cdot 2 + 5 s}{2} + 20 = 62$

Step 1.1.6

Add $s \cdot 2$ and $5 s$ .

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Step 1.1.6.1

Reorder $s$ and $2$ .

$\frac{2 \cdot s + 5 s}{2} + 20 = 62$

Step 1.1.6.2

Add $2 \cdot s$ and $5 s$ .

$\frac{7 \cdot s}{2} + 20 = 62$

$\frac{7 s}{2} + 20 = 62$

Step 2

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

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Step 2.1

Subtract $20$ from both sides of the equation.

$\frac{7 s}{2} = 62 - 20$

Step 2.2

Subtract $20$ from $62$ .

$\frac{7 s}{2} = 42$

Step 3

Multiply both sides of the equation by $\frac{2}{7}$ .

$\frac{2}{7} \cdot \frac{7 s}{2} = \frac{2}{7} \cdot 42$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{2}{7} \cdot \frac{7 s}{2}$ .

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Step 4.1.1.1

Cancel the common factor of $2$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{2}{7} \cdot \frac{7 s}{2} = \frac{2}{7} \cdot 42$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{7} (7 s) = \frac{2}{7} \cdot 42$

Step 4.1.1.2

Cancel the common factor of $7$ .

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Step 4.1.1.2.1

Factor $7$ out of $7 s$ .

$\frac{1}{7} (7 (s)) = \frac{2}{7} \cdot 42$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{7} (7 s) = \frac{2}{7} \cdot 42$

Step 4.1.1.2.3

Rewrite the expression.

$s = \frac{2}{7} \cdot 42$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{2}{7} \cdot 42$ .

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Step 4.2.1.1

Cancel the common factor of $7$ .

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Step 4.2.1.1.1

Factor $7$ out of $42$ .

$s = \frac{2}{7} \cdot (7 (6))$

Step 4.2.1.1.2

Cancel the common factor.

$s = \frac{2}{7} \cdot (7 \cdot 6)$

Step 4.2.1.1.3

Rewrite the expression.

$s = 2 \cdot 6$

Step 4.2.1.2

Multiply $2$ by $6$ .

$s = 12$