Basic Math Examples

$0.5 s + \frac{4}{3} s = s + 10$

Step 1

Simplify $0.5 s + \frac{4}{3} s$ .

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Step 1.1

Combine $\frac{4}{3}$ and $s$ .

$0.5 s + \frac{4 s}{3} = s + 10$

Step 1.2

To write $0.5 s$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$0.5 s \cdot \frac{3}{3} + \frac{4 s}{3} = s + 10$

Step 1.3

Simplify terms.

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Step 1.3.1

Combine $0.5 s$ and $\frac{3}{3}$ .

$\frac{0.5 s \cdot 3}{3} + \frac{4 s}{3} = s + 10$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{0.5 s \cdot 3 + 4 s}{3} = s + 10$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Factor $0.5 s$ out of $0.5 s \cdot 3 + 4 s$ .

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Step 1.4.1.1

Move $s$ .

$\frac{0.5 \cdot 3 s + 4 s}{3} = s + 10$

Step 1.4.1.2

Factor $0.5 s$ out of $0.5 \cdot 3 s$ .

$\frac{0.5 s (3) + 4 s}{3} = s + 10$

Step 1.4.1.3

Factor $0.5 s$ out of $4 s$ .

$\frac{0.5 s (3) + 0.5 s (8)}{3} = s + 10$

Step 1.4.1.4

Factor $0.5 s$ out of $0.5 s (3) + 0.5 s (8)$ .

$\frac{0.5 s (3 + 8)}{3} = s + 10$

Step 1.4.2

Multiply $3 + 8$ by $0.5$ .

$\frac{5.5 s}{3} = s + 10$

Step 1.5

Simplify with factoring out.

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Step 1.5.1

Factor $5.5$ out of $5.5 s$ .

$\frac{5.5 (s)}{3} = s + 10$

Step 1.5.2

Factor $3$ out of $3$ .

$\frac{5.5 (s)}{3 (1)} = s + 10$

Step 1.6

Separate fractions.

$\frac{5.5}{3} \cdot \frac{s}{1} = s + 10$

Step 1.7

Divide $5.5$ by $3$ .

$1.8\overline{3} \frac{s}{1} = s + 10$

Step 1.8

Divide $s$ by $1$ .

$1.8\overline{3} s = s + 10$

Step 2

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

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Step 2.1

Subtract $s$ from both sides of the equation.

$1.8\overline{3} s - s = 10$

Step 2.2

Subtract $s$ from $1.8\overline{3} s$ .

$0.8\overline{3} s = 10$

Step 3

Divide each term in $0.8\overline{3} s = 10$ by $0.8\overline{3}$ and simplify.

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Step 3.1

Divide each term in $0.8\overline{3} s = 10$ by $0.8\overline{3}$ .

$\frac{0.8\overline{3} s}{0.8\overline{3}} = \frac{10}{0.8\overline{3}}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $0.8\overline{3}$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{0.8\overline{3} s}{0.8\overline{3}} = \frac{10}{0.8\overline{3}}$

Step 3.2.1.2

Divide $s$ by $1$ .

$s = \frac{10}{0.8\overline{3}}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $10$ by $0.8\overline{3}$ .

$s = 12$