Algebra Examples

$\frac{3 d}{8} = 6 r + 1$

Step 1

Multiply both sides of the equation by $\frac{8}{3}$ .

$\frac{8}{3} \cdot \frac{3 d}{8} = \frac{8}{3} (6 r + 1)$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{8}{3} \cdot \frac{3 d}{8}$ .

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Step 2.1.1.1

Cancel the common factor of $8$ .

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Step 2.1.1.1.1

Cancel the common factor.

$\frac{8}{3} \cdot \frac{3 d}{8} = \frac{8}{3} (6 r + 1)$

Step 2.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 d) = \frac{8}{3} (6 r + 1)$

Step 2.1.1.2

Cancel the common factor of $3$ .

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Step 2.1.1.2.1

Factor $3$ out of $3 d$ .

$\frac{1}{3} (3 (d)) = \frac{8}{3} (6 r + 1)$

Step 2.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 d) = \frac{8}{3} (6 r + 1)$

Step 2.1.1.2.3

Rewrite the expression.

$d = \frac{8}{3} (6 r + 1)$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{8}{3} (6 r + 1)$ .

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Step 2.2.1.1

Apply the distributive property.

$d = \frac{8}{3} (6 r) + \frac{8}{3} \cdot 1$

Step 2.2.1.2

Cancel the common factor of $3$ .

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Step 2.2.1.2.1

Factor $3$ out of $6 r$ .

$d = \frac{8}{3} (3 (2 r)) + \frac{8}{3} \cdot 1$

Step 2.2.1.2.2

Cancel the common factor.

$d = \frac{8}{3} (3 (2 r)) + \frac{8}{3} \cdot 1$

Step 2.2.1.2.3

Rewrite the expression.

$d = 8 (2 r) + \frac{8}{3} \cdot 1$

Step 2.2.1.3

Multiply.

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Step 2.2.1.3.1

Multiply $2$ by $8$ .

$d = 16 r + \frac{8}{3} \cdot 1$

Step 2.2.1.3.2

Multiply $\frac{8}{3}$ by $1$ .

$d = 16 r + \frac{8}{3}$