Algebra Examples

$\frac{5}{8} - \frac{3}{8} s = 2 - s$

Step 1

Simplify each term.

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Step 1.1

Combine $s$ and $\frac{3}{8}$ .

$\frac{5}{8} - \frac{s \cdot 3}{8} = 2 - s$

Step 1.2

Move $3$ to the left of $s$ .

$\frac{5}{8} - \frac{3 s}{8} = 2 - s$

Step 2

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

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Step 2.1

Add $s$ to both sides of the equation.

$\frac{5}{8} - \frac{3 s}{8} + s = 2$

Step 2.2

To write $s$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{5}{8} - \frac{3 s}{8} + s \cdot \frac{8}{8} = 2$

Step 2.3

Combine $s$ and $\frac{8}{8}$ .

$\frac{5}{8} - \frac{3 s}{8} + \frac{s \cdot 8}{8} = 2$

Step 2.4

Combine the numerators over the common denominator.

$\frac{5}{8} + \frac{- 3 s + s \cdot 8}{8} = 2$

Step 2.5

Combine the numerators over the common denominator.

$\frac{5 - 3 s + s \cdot 8}{8} = 2$

Step 2.6

Move $8$ to the left of $s$ .

$\frac{5 - 3 s + 8 s}{8} = 2$

Step 2.7

Add $- 3 s$ and $8 s$ .

$\frac{5 + 5 s}{8} = 2$

Step 2.8

Factor $5$ out of $5 + 5 s$ .

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Step 2.8.1

Factor $5$ out of $5$ .

$\frac{5 \cdot 1 + 5 s}{8} = 2$

Step 2.8.2

Factor $5$ out of $5 \cdot 1 + 5 s$ .

$\frac{5 (1 + s)}{8} = 2$

Step 3

Multiply both sides of the equation by $\frac{8}{5}$ .

$\frac{8}{5} \cdot \frac{5 (1 + s)}{8} = \frac{8}{5} \cdot 2$

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 $\frac{8}{5} \cdot \frac{5 (1 + s)}{8}$ .

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Step 4.1.1.1

Cancel the common factor of $8$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{8}{5} \cdot \frac{5 (1 + s)}{8} = \frac{8}{5} \cdot 2$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 (1 + s)) = \frac{8}{5} \cdot 2$

Step 4.1.1.2

Cancel the common factor of $5$ .

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Step 4.1.1.2.1

Cancel the common factor.

$\frac{1}{5} (5 (1 + s)) = \frac{8}{5} \cdot 2$

Step 4.1.1.2.2

Rewrite the expression.

$1 + s = \frac{8}{5} \cdot 2$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $\frac{8}{5} \cdot 2$ .

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Step 4.2.1.1

Combine $\frac{8}{5}$ and $2$ .

$1 + s = \frac{8 \cdot 2}{5}$

Step 4.2.1.2

Multiply $8$ by $2$ .

$1 + s = \frac{16}{5}$

Step 5

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

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Step 5.1

Subtract $1$ from both sides of the equation.

$s = \frac{16}{5} - 1$

Step 5.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$s = \frac{16}{5} - 1 \cdot \frac{5}{5}$

Step 5.3

Combine $- 1$ and $\frac{5}{5}$ .

$s = \frac{16}{5} + \frac{- 1 \cdot 5}{5}$

Step 5.4

Combine the numerators over the common denominator.

$s = \frac{16 - 1 \cdot 5}{5}$

Step 5.5

Simplify the numerator.

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Step 5.5.1

Multiply $- 1$ by $5$ .

$s = \frac{16 - 5}{5}$

Step 5.5.2

Subtract $5$ from $16$ .

$s = \frac{11}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$s = \frac{11}{5}$

Decimal Form:

$s = 2.2$

Mixed Number Form:

$s = 2 \frac{1}{5}$