Algebra Examples

$\frac{4}{9} (\frac{3}{8} x - \frac{27}{16}) = \frac{13}{4}$

Step 1

Multiply both sides of the equation by $\frac{9}{4}$ .

$\frac{9}{4} (\frac{4}{9} \cdot (\frac{3}{8} x - \frac{27}{16})) = \frac{9}{4} \cdot \frac{13}{4}$

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 $\frac{9}{4} (\frac{4}{9} \cdot (\frac{3}{8} x - \frac{27}{16}))$ .

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Step 2.1.1.1

Combine $\frac{3}{8}$ and $x$ .

$\frac{9}{4} (\frac{4}{9} \cdot (\frac{3 x}{8} - \frac{27}{16})) = \frac{9}{4} \cdot \frac{13}{4}$

Step 2.1.1.2

Apply the distributive property.

$\frac{9}{4} (\frac{4}{9} \cdot \frac{3 x}{8} + \frac{4}{9} (- \frac{27}{16})) = \frac{9}{4} \cdot \frac{13}{4}$

Step 2.1.1.3

Cancel the common factor of $4$ .

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Step 2.1.1.3.1

Factor $4$ out of $8$ .

$\frac{9}{4} (\frac{4}{9} \cdot \frac{3 x}{4 (2)} + \frac{4}{9} (- \frac{27}{16})) = \frac{9}{4} \cdot \frac{13}{4}$

Step 2.1.1.3.2

Cancel the common factor.

$\frac{9}{4} (\frac{4}{9} \cdot \frac{3 x}{4 \cdot 2} + \frac{4}{9} (- \frac{27}{16})) = \frac{9}{4} \cdot \frac{13}{4}$

Step 2.1.1.3.3

Rewrite the expression.

$\frac{9}{4} (\frac{1}{9} \cdot \frac{3 x}{2} + \frac{4}{9} (- \frac{27}{16})) = \frac{9}{4} \cdot \frac{13}{4}$

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 $9$ .

$\frac{9}{4} (\frac{1}{3 (3)} \cdot \frac{3 x}{2} + \frac{4}{9} (- \frac{27}{16})) = \frac{9}{4} \cdot \frac{13}{4}$

Step 2.1.1.4.2

Factor $3$ out of $3 x$ .

$\frac{9}{4} (\frac{1}{3 (3)} \cdot \frac{3 (x)}{2} + \frac{4}{9} (- \frac{27}{16})) = \frac{9}{4} \cdot \frac{13}{4}$

Step 2.1.1.4.3

Cancel the common factor.

$\frac{9}{4} (\frac{1}{3 \cdot 3} \cdot \frac{3 x}{2} + \frac{4}{9} (- \frac{27}{16})) = \frac{9}{4} \cdot \frac{13}{4}$

Step 2.1.1.4.4

Rewrite the expression.

$\frac{9}{4} (\frac{1}{3} \cdot \frac{x}{2} + \frac{4}{9} (- \frac{27}{16})) = \frac{9}{4} \cdot \frac{13}{4}$

Step 2.1.1.5

Multiply $\frac{1}{3}$ by $\frac{x}{2}$ .

$\frac{9}{4} (\frac{x}{3 \cdot 2} + \frac{4}{9} (- \frac{27}{16})) = \frac{9}{4} \cdot \frac{13}{4}$

Step 2.1.1.6

Multiply $3$ by $2$ .

$\frac{9}{4} (\frac{x}{6} + \frac{4}{9} (- \frac{27}{16})) = \frac{9}{4} \cdot \frac{13}{4}$

Step 2.1.1.7

Cancel the common factor of $4$ .

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Step 2.1.1.7.1

Move the leading negative in $- \frac{27}{16}$ into the numerator.

$\frac{9}{4} (\frac{x}{6} + \frac{4}{9} \cdot \frac{- 27}{16}) = \frac{9}{4} \cdot \frac{13}{4}$

Step 2.1.1.7.2

Factor $4$ out of $16$ .

$\frac{9}{4} (\frac{x}{6} + \frac{4}{9} \cdot \frac{- 27}{4 (4)}) = \frac{9}{4} \cdot \frac{13}{4}$

Step 2.1.1.7.3

Cancel the common factor.

$\frac{9}{4} (\frac{x}{6} + \frac{4}{9} \cdot \frac{- 27}{4 \cdot 4}) = \frac{9}{4} \cdot \frac{13}{4}$

Step 2.1.1.7.4

Rewrite the expression.

$\frac{9}{4} (\frac{x}{6} + \frac{1}{9} \cdot \frac{- 27}{4}) = \frac{9}{4} \cdot \frac{13}{4}$

Step 2.1.1.8

Cancel the common factor of $9$ .

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Step 2.1.1.8.1

Factor $9$ out of $- 27$ .

$\frac{9}{4} (\frac{x}{6} + \frac{1}{9} \cdot \frac{9 (- 3)}{4}) = \frac{9}{4} \cdot \frac{13}{4}$

Step 2.1.1.8.2

Cancel the common factor.

$\frac{9}{4} (\frac{x}{6} + \frac{1}{9} \cdot \frac{9 \cdot - 3}{4}) = \frac{9}{4} \cdot \frac{13}{4}$

Step 2.1.1.8.3

Rewrite the expression.

$\frac{9}{4} (\frac{x}{6} + \frac{- 3}{4}) = \frac{9}{4} \cdot \frac{13}{4}$

Step 2.1.1.9

Move the negative in front of the fraction.

$\frac{9}{4} (\frac{x}{6} - \frac{3}{4}) = \frac{9}{4} \cdot \frac{13}{4}$

Step 2.1.1.10

Apply the distributive property.

$\frac{9}{4} \cdot \frac{x}{6} + \frac{9}{4} (- \frac{3}{4}) = \frac{9}{4} \cdot \frac{13}{4}$

Step 2.1.1.11

Cancel the common factor of $3$ .

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Step 2.1.1.11.1

Factor $3$ out of $9$ .

$\frac{3 (3)}{4} \cdot \frac{x}{6} + \frac{9}{4} (- \frac{3}{4}) = \frac{9}{4} \cdot \frac{13}{4}$

Step 2.1.1.11.2

Factor $3$ out of $6$ .

$\frac{3 \cdot 3}{4} \cdot \frac{x}{3 \cdot 2} + \frac{9}{4} (- \frac{3}{4}) = \frac{9}{4} \cdot \frac{13}{4}$

Step 2.1.1.11.3

Cancel the common factor.

$\frac{3 \cdot 3}{4} \cdot \frac{x}{3 \cdot 2} + \frac{9}{4} (- \frac{3}{4}) = \frac{9}{4} \cdot \frac{13}{4}$

Step 2.1.1.11.4

Rewrite the expression.

$\frac{3}{4} \cdot \frac{x}{2} + \frac{9}{4} (- \frac{3}{4}) = \frac{9}{4} \cdot \frac{13}{4}$

Step 2.1.1.12

Multiply $\frac{3}{4}$ by $\frac{x}{2}$ .

$\frac{3 x}{4 \cdot 2} + \frac{9}{4} (- \frac{3}{4}) = \frac{9}{4} \cdot \frac{13}{4}$

Step 2.1.1.13

Multiply $4$ by $2$ .

$\frac{3 x}{8} + \frac{9}{4} (- \frac{3}{4}) = \frac{9}{4} \cdot \frac{13}{4}$

Step 2.1.1.14

Multiply $\frac{9}{4} (- \frac{3}{4})$ .

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Step 2.1.1.14.1

Multiply $\frac{9}{4}$ by $\frac{3}{4}$ .

$\frac{3 x}{8} - \frac{9 \cdot 3}{4 \cdot 4} = \frac{9}{4} \cdot \frac{13}{4}$

Step 2.1.1.14.2

Multiply $9$ by $3$ .

$\frac{3 x}{8} - \frac{27}{4 \cdot 4} = \frac{9}{4} \cdot \frac{13}{4}$

Step 2.1.1.14.3

Multiply $4$ by $4$ .

$\frac{3 x}{8} - \frac{27}{16} = \frac{9}{4} \cdot \frac{13}{4}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $\frac{9}{4} \cdot \frac{13}{4}$ .

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Step 2.2.1.1

Multiply $\frac{9}{4}$ by $\frac{13}{4}$ .

$\frac{3 x}{8} - \frac{27}{16} = \frac{9 \cdot 13}{4 \cdot 4}$

Step 2.2.1.2

Multiply $9$ by $13$ .

$\frac{3 x}{8} - \frac{27}{16} = \frac{117}{4 \cdot 4}$

Step 2.2.1.3

Multiply $4$ by $4$ .

$\frac{3 x}{8} - \frac{27}{16} = \frac{117}{16}$

Step 3

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

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Step 3.1

Add $\frac{27}{16}$ to both sides of the equation.

$\frac{3 x}{8} = \frac{117}{16} + \frac{27}{16}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{3 x}{8} = \frac{117 + 27}{16}$

Step 3.3

Add $117$ and $27$ .

$\frac{3 x}{8} = \frac{144}{16}$

Step 3.4

Divide $144$ by $16$ .

$\frac{3 x}{8} = 9$

Step 4

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

$\frac{8}{3} \cdot \frac{3 x}{8} = \frac{8}{3} \cdot 9$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

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

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Step 5.1.1.1

Cancel the common factor of $8$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{8}{3} \cdot \frac{3 x}{8} = \frac{8}{3} \cdot 9$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 x) = \frac{8}{3} \cdot 9$

Step 5.1.1.2

Cancel the common factor of $3$ .

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Step 5.1.1.2.1

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{8}{3} \cdot 9$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{8}{3} \cdot 9$

Step 5.1.1.2.3

Rewrite the expression.

$x = \frac{8}{3} \cdot 9$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{8}{3} \cdot 9$ .

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Step 5.2.1.1

Cancel the common factor of $3$ .

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Step 5.2.1.1.1

Factor $3$ out of $9$ .

$x = \frac{8}{3} \cdot (3 (3))$

Step 5.2.1.1.2

Cancel the common factor.

$x = \frac{8}{3} \cdot (3 \cdot 3)$

Step 5.2.1.1.3

Rewrite the expression.

$x = 8 \cdot 3$

Step 5.2.1.2

Multiply $8$ by $3$ .

$x = 24$