Algebra Examples

$\frac{2}{3} (6 a + 9) = 20.4$

Step 1

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

$\frac{3}{2} (\frac{2}{3} \cdot (6 a + 9)) = \frac{3}{2} \cdot 20.4$

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 $\frac{3}{2} (\frac{2}{3} \cdot (6 a + 9))$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{3}{2} (\frac{2}{3} (6 a) + \frac{2}{3} \cdot 9) = \frac{3}{2} \cdot 20.4$

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 $6 a$ .

$\frac{3}{2} (\frac{2}{3} (3 (2 a)) + \frac{2}{3} \cdot 9) = \frac{3}{2} \cdot 20.4$

Step 2.1.1.2.2

Cancel the common factor.

$\frac{3}{2} (\frac{2}{3} (3 (2 a)) + \frac{2}{3} \cdot 9) = \frac{3}{2} \cdot 20.4$

Step 2.1.1.2.3

Rewrite the expression.

$\frac{3}{2} (2 (2 a) + \frac{2}{3} \cdot 9) = \frac{3}{2} \cdot 20.4$

Step 2.1.1.3

Multiply $2$ by $2$ .

$\frac{3}{2} (4 a + \frac{2}{3} \cdot 9) = \frac{3}{2} \cdot 20.4$

Step 2.1.1.4

Cancel the common factor of $3$ .

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Step 2.1.1.4.1

Factor $3$ out of $9$ .

$\frac{3}{2} (4 a + \frac{2}{3} \cdot (3 (3))) = \frac{3}{2} \cdot 20.4$

Step 2.1.1.4.2

Cancel the common factor.

$\frac{3}{2} (4 a + \frac{2}{3} \cdot (3 \cdot 3)) = \frac{3}{2} \cdot 20.4$

Step 2.1.1.4.3

Rewrite the expression.

$\frac{3}{2} (4 a + 2 \cdot 3) = \frac{3}{2} \cdot 20.4$

Step 2.1.1.5

Multiply $2$ by $3$ .

$\frac{3}{2} (4 a + 6) = \frac{3}{2} \cdot 20.4$

Step 2.1.1.6

Apply the distributive property.

$\frac{3}{2} (4 a) + \frac{3}{2} \cdot 6 = \frac{3}{2} \cdot 20.4$

Step 2.1.1.7

Cancel the common factor of $2$ .

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Step 2.1.1.7.1

Factor $2$ out of $4 a$ .

$\frac{3}{2} (2 (2 a)) + \frac{3}{2} \cdot 6 = \frac{3}{2} \cdot 20.4$

Step 2.1.1.7.2

Cancel the common factor.

$\frac{3}{2} (2 (2 a)) + \frac{3}{2} \cdot 6 = \frac{3}{2} \cdot 20.4$

Step 2.1.1.7.3

Rewrite the expression.

$3 (2 a) + \frac{3}{2} \cdot 6 = \frac{3}{2} \cdot 20.4$

Step 2.1.1.8

Multiply $2$ by $3$ .

$6 a + \frac{3}{2} \cdot 6 = \frac{3}{2} \cdot 20.4$

Step 2.1.1.9

Cancel the common factor of $2$ .

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Step 2.1.1.9.1

Factor $2$ out of $6$ .

$6 a + \frac{3}{2} \cdot (2 (3)) = \frac{3}{2} \cdot 20.4$

Step 2.1.1.9.2

Cancel the common factor.

$6 a + \frac{3}{2} \cdot (2 \cdot 3) = \frac{3}{2} \cdot 20.4$

Step 2.1.1.9.3

Rewrite the expression.

$6 a + 3 \cdot 3 = \frac{3}{2} \cdot 20.4$

Step 2.1.1.10

Multiply $3$ by $3$ .

$6 a + 9 = \frac{3}{2} \cdot 20.4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{3}{2} \cdot 20.4$ .

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Step 2.2.1.1

Multiply $\frac{3}{2} \cdot 20.4$ .

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Step 2.2.1.1.1

Combine $\frac{3}{2}$ and $20.4$ .

$6 a + 9 = \frac{3 \cdot 20.4}{2}$

Step 2.2.1.1.2

Multiply $3$ by $20.4$ .

$6 a + 9 = \frac{61.2}{2}$

Step 2.2.1.2

Divide $61.2$ by $2$ .

$6 a + 9 = 30.6$

Step 3

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

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Step 3.1

Subtract $9$ from both sides of the equation.

$6 a = 30.6 - 9$

Step 3.2

Subtract $9$ from $30.6$ .

$6 a = 21.6$

Step 4

Divide each term in $6 a = 21.6$ by $6$ and simplify.

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Step 4.1

Divide each term in $6 a = 21.6$ by $6$ .

$\frac{6 a}{6} = \frac{21.6}{6}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $6$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{6 a}{6} = \frac{21.6}{6}$

Step 4.2.1.2

Divide $a$ by $1$ .

$a = \frac{21.6}{6}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $21.6$ by $6$ .

$a = 3.6$