Algebra Examples

$\frac{2}{3} (F + G) = D$

Step 1

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} (\frac{2}{3} \cdot (F + G)) = \frac{3}{2} D$

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 $\frac{3}{2} (\frac{2}{3} \cdot (F + G))$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{3}{2} (\frac{2}{3} F + \frac{2}{3} G) = \frac{3}{2} D$

Step 2.1.1.2

Combine $\frac{2}{3}$ and $F$ .

$\frac{3}{2} (\frac{2 F}{3} + \frac{2}{3} G) = \frac{3}{2} D$

Step 2.1.1.3

Combine $\frac{2}{3}$ and $G$ .

$\frac{3}{2} (\frac{2 F}{3} + \frac{2 G}{3}) = \frac{3}{2} D$

Step 2.1.1.4

Apply the distributive property.

$\frac{3}{2} \cdot \frac{2 F}{3} + \frac{3}{2} \cdot \frac{2 G}{3} = \frac{3}{2} D$

Step 2.1.1.5

Cancel the common factor of $3$ .

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Step 2.1.1.5.1

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 F}{3} + \frac{3}{2} \cdot \frac{2 G}{3} = \frac{3}{2} D$

Step 2.1.1.5.2

Rewrite the expression.

$\frac{1}{2} (2 F) + \frac{3}{2} \cdot \frac{2 G}{3} = \frac{3}{2} D$

Step 2.1.1.6

Cancel the common factor of $2$ .

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Step 2.1.1.6.1

Factor $2$ out of $2 F$ .

$\frac{1}{2} (2 (F)) + \frac{3}{2} \cdot \frac{2 G}{3} = \frac{3}{2} D$

Step 2.1.1.6.2

Cancel the common factor.

$\frac{1}{2} (2 F) + \frac{3}{2} \cdot \frac{2 G}{3} = \frac{3}{2} D$

Step 2.1.1.6.3

Rewrite the expression.

$F + \frac{3}{2} \cdot \frac{2 G}{3} = \frac{3}{2} D$

Step 2.1.1.7

Cancel the common factor of $3$ .

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Step 2.1.1.7.1

Cancel the common factor.

$F + \frac{3}{2} \cdot \frac{2 G}{3} = \frac{3}{2} D$

Step 2.1.1.7.2

Rewrite the expression.

$F + \frac{1}{2} (2 G) = \frac{3}{2} D$

Step 2.1.1.8

Cancel the common factor of $2$ .

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Step 2.1.1.8.1

Factor $2$ out of $2 G$ .

$F + \frac{1}{2} (2 (G)) = \frac{3}{2} D$

Step 2.1.1.8.2

Cancel the common factor.

$F + \frac{1}{2} (2 G) = \frac{3}{2} D$

Step 2.1.1.8.3

Rewrite the expression.

$F + G = \frac{3}{2} D$

Step 2.2

Simplify the right side.

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Step 2.2.1

Combine $\frac{3}{2}$ and $D$ .

$F + G = \frac{3 D}{2}$

Step 3

Subtract $G$ from both sides of the equation.

$F = \frac{3 D}{2} - G$