Basic Math Examples

\frac{3}{5} d + 5 = \frac{1}{3} d - 3

$\frac{3}{5} d + 5 = \frac{1}{3} d - 3$

Step 1

Combine

\frac{3}{5}

$\frac{3}{5}$ and

d

$d$ .

\frac{3 d}{5} + 5 = \frac{1}{3} d - 3

$\frac{3 d}{5} + 5 = \frac{1}{3} d - 3$

Step 2

Combine

\frac{1}{3}

$\frac{1}{3}$ and

d

$d$ .

\frac{3 d}{5} + 5 = \frac{d}{3} - 3

$\frac{3 d}{5} + 5 = \frac{d}{3} - 3$

Step 3

Move all terms containing

d

$d$ to the left side of the equation.

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Step 3.1

Subtract

\frac{d}{3}

$\frac{d}{3}$ from both sides of the equation.

\frac{3 d}{5} + 5 - \frac{d}{3} = - 3

$\frac{3 d}{5} + 5 - \frac{d}{3} = - 3$

Step 3.2

To write

\frac{3 d}{5}

$\frac{3 d}{5}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{3 d}{5} \cdot \frac{3}{3} - \frac{d}{3} + 5 = - 3

$\frac{3 d}{5} \cdot \frac{3}{3} - \frac{d}{3} + 5 = - 3$

Step 3.3

To write

- \frac{d}{3}

$- \frac{d}{3}$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{3 d}{5} \cdot \frac{3}{3} - \frac{d}{3} \cdot \frac{5}{5} + 5 = - 3

$\frac{3 d}{5} \cdot \frac{3}{3} - \frac{d}{3} \cdot \frac{5}{5} + 5 = - 3$

Step 3.4

Write each expression with a common denominator of

15

$15$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.4.1

Multiply

\frac{3 d}{5}

$\frac{3 d}{5}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{3 d \cdot 3}{5 \cdot 3} - \frac{d}{3} \cdot \frac{5}{5} + 5 = - 3

$\frac{3 d \cdot 3}{5 \cdot 3} - \frac{d}{3} \cdot \frac{5}{5} + 5 = - 3$

Step 3.4.2

Multiply

5

$5$ by

3

$3$ .

\frac{3 d \cdot 3}{15} - \frac{d}{3} \cdot \frac{5}{5} + 5 = - 3

$\frac{3 d \cdot 3}{15} - \frac{d}{3} \cdot \frac{5}{5} + 5 = - 3$

Step 3.4.3

Multiply

\frac{d}{3}

$\frac{d}{3}$ by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{3 d \cdot 3}{15} - \frac{d \cdot 5}{3 \cdot 5} + 5 = - 3

$\frac{3 d \cdot 3}{15} - \frac{d \cdot 5}{3 \cdot 5} + 5 = - 3$

Step 3.4.4

Multiply

3

$3$ by

5

$5$ .

\frac{3 d \cdot 3}{15} - \frac{d \cdot 5}{15} + 5 = - 3

$\frac{3 d \cdot 3}{15} - \frac{d \cdot 5}{15} + 5 = - 3$

\frac{3 d \cdot 3}{15} - \frac{d \cdot 5}{15} + 5 = - 3

$\frac{3 d \cdot 3}{15} - \frac{d \cdot 5}{15} + 5 = - 3$

Step 3.5

Combine the numerators over the common denominator.

\frac{3 d \cdot 3 - d \cdot 5}{15} + 5 = - 3

$\frac{3 d \cdot 3 - d \cdot 5}{15} + 5 = - 3$

Step 3.6

Simplify each term.

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Step 3.6.1

Simplify the numerator.

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Step 3.6.1.1

Factor

d

$d$ out of

3 d \cdot 3 - d \cdot 5

$3 d \cdot 3 - d \cdot 5$ .

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Step 3.6.1.1.1

Factor

d

$d$ out of

3 d \cdot 3

$3 d \cdot 3$ .

\frac{d (3 \cdot 3) - d \cdot 5}{15} + 5 = - 3

$\frac{d (3 \cdot 3) - d \cdot 5}{15} + 5 = - 3$

Step 3.6.1.1.2

Factor

d

$d$ out of

- d \cdot 5

$- d \cdot 5$ .

\frac{d (3 \cdot 3) + d (- 1 \cdot 5)}{15} + 5 = - 3

$\frac{d (3 \cdot 3) + d (- 1 \cdot 5)}{15} + 5 = - 3$

Step 3.6.1.1.3

Factor

d

$d$ out of

d (3 \cdot 3) + d (- 1 \cdot 5)

$d (3 \cdot 3) + d (- 1 \cdot 5)$ .

\frac{d (3 \cdot 3 - 1 \cdot 5)}{15} + 5 = - 3

$\frac{d (3 \cdot 3 - 1 \cdot 5)}{15} + 5 = - 3$

\frac{d (3 \cdot 3 - 1 \cdot 5)}{15} + 5 = - 3

$\frac{d (3 \cdot 3 - 1 \cdot 5)}{15} + 5 = - 3$

Step 3.6.1.2

Multiply

3

$3$ by

3

$3$ .

\frac{d (9 - 1 \cdot 5)}{15} + 5 = - 3

$\frac{d (9 - 1 \cdot 5)}{15} + 5 = - 3$

Step 3.6.1.3

Multiply

- 1

$- 1$ by

5

$5$ .

\frac{d (9 - 5)}{15} + 5 = - 3

$\frac{d (9 - 5)}{15} + 5 = - 3$

Step 3.6.1.4

Subtract

5

$5$ from

9

$9$ .

\frac{d \cdot 4}{15} + 5 = - 3

$\frac{d \cdot 4}{15} + 5 = - 3$

\frac{d \cdot 4}{15} + 5 = - 3

$\frac{d \cdot 4}{15} + 5 = - 3$

Step 3.6.2

Move

4

$4$ to the left of

d

$d$ .

\frac{4 d}{15} + 5 = - 3

$\frac{4 d}{15} + 5 = - 3$

\frac{4 d}{15} + 5 = - 3

$\frac{4 d}{15} + 5 = - 3$

Step 4

Move all terms not containing

$d$ to the right side of the equation.

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Step 4.1

Subtract

$5$ from both sides of the equation.

$\frac{4 d}{15} = - 3 - 5$

Step 4.2

Subtract

$5$ from

$- 3$ .

$\frac{4 d}{15} = - 8$

Step 5

Multiply both sides of the equation by

$\frac{15}{4}$ .

$\frac{15}{4} \cdot \frac{4 d}{15} = \frac{15}{4} \cdot - 8$

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

Simplify

$\frac{15}{4} \cdot \frac{4 d}{15}$ .

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Step 6.1.1.1

Cancel the common factor of

$15$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{15}{4} \cdot \frac{4 d}{15} = \frac{15}{4} \cdot - 8$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{4} (4 d) = \frac{15}{4} \cdot - 8$

Step 6.1.1.2

Cancel the common factor of

$4$ .

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Step 6.1.1.2.1

Factor

$4$ out of

$4 d$ .

$\frac{1}{4} (4 (d)) = \frac{15}{4} \cdot - 8$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{4} (4 d) = \frac{15}{4} \cdot - 8$

Step 6.1.1.2.3

Rewrite the expression.

$d = \frac{15}{4} \cdot - 8$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify

$\frac{15}{4} \cdot - 8$ .

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Step 6.2.1.1

Cancel the common factor of

$4$ .

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Step 6.2.1.1.1

Factor

$4$ out of

$- 8$ .

$d = \frac{15}{4} \cdot (4 (- 2))$

Step 6.2.1.1.2

Cancel the common factor.

$d = \frac{15}{4} \cdot (4 \cdot - 2)$

Step 6.2.1.1.3

Rewrite the expression.

$d = 15 \cdot - 2$

Step 6.2.1.2

Multiply

$15$ by

$- 2$ .

$d = - 30$