Algebra Examples

$(8 x - 8) \frac{3}{2} = 64$

Step 1

Multiply $8 x - 8$ by $\frac{3}{2}$ .

$(8 x - 8) \frac{3}{2} = 64$

Step 2

Multiply each term in $(8 x - 8) (\frac{3}{2}) = 64$ by $\frac{2}{3}$ to eliminate the fractions.

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Step 2.1

Multiply each term in $(8 x - 8) (\frac{3}{2}) = 64$ by $\frac{2}{3}$ .

$(8 x - 8) \frac{3}{2} \frac{2}{3} = 64 (\frac{2}{3})$

Step 2.2

Simplify the left side.

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Step 2.2.1

Apply the distributive property.

$(8 x \frac{3}{2} - 8 (\frac{3}{2})) \frac{2}{3} = 64 (\frac{2}{3})$

Step 2.2.2

Cancel the common factor of $2$ .

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Step 2.2.2.1

Factor $2$ out of $8 x$ .

$(2 (4 x) \frac{3}{2} - 8 (\frac{3}{2})) \frac{2}{3} = 64 (\frac{2}{3})$

Step 2.2.2.2

Cancel the common factor.

$(2 (4 x) \frac{3}{2} - 8 (\frac{3}{2})) \frac{2}{3} = 64 (\frac{2}{3})$

Step 2.2.2.3

Rewrite the expression.

$(4 x \cdot 3 - 8 (\frac{3}{2})) \frac{2}{3} = 64 (\frac{2}{3})$

Step 2.2.3

Multiply $3$ by $4$ .

$(12 x - 8 (\frac{3}{2})) \frac{2}{3} = 64 (\frac{2}{3})$

Step 2.2.4

Cancel the common factor of $2$ .

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Step 2.2.4.1

Factor $2$ out of $- 8$ .

$(12 x + 2 (- 4) \frac{3}{2}) \frac{2}{3} = 64 (\frac{2}{3})$

Step 2.2.4.2

Cancel the common factor.

$(12 x + 2 \cdot - 4 \frac{3}{2}) \frac{2}{3} = 64 (\frac{2}{3})$

Step 2.2.4.3

Rewrite the expression.

$(12 x - 4 \cdot 3) \frac{2}{3} = 64 (\frac{2}{3})$

Step 2.2.5

Multiply $- 4$ by $3$ .

$(12 x - 12) \frac{2}{3} = 64 (\frac{2}{3})$

Step 2.2.6

Apply the distributive property.

$12 x \frac{2}{3} - 12 (\frac{2}{3}) = 64 (\frac{2}{3})$

Step 2.2.7

Cancel the common factor of $3$ .

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Step 2.2.7.1

Factor $3$ out of $12 x$ .

$3 (4 x) \frac{2}{3} - 12 (\frac{2}{3}) = 64 (\frac{2}{3})$

Step 2.2.7.2

Cancel the common factor.

$3 (4 x) \frac{2}{3} - 12 (\frac{2}{3}) = 64 (\frac{2}{3})$

Step 2.2.7.3

Rewrite the expression.

$4 x \cdot 2 - 12 (\frac{2}{3}) = 64 (\frac{2}{3})$

Step 2.2.8

Multiply $2$ by $4$ .

$8 x - 12 (\frac{2}{3}) = 64 (\frac{2}{3})$

Step 2.2.9

Cancel the common factor of $3$ .

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Step 2.2.9.1

Factor $3$ out of $- 12$ .

$8 x + 3 (- 4) \frac{2}{3} = 64 (\frac{2}{3})$

Step 2.2.9.2

Cancel the common factor.

$8 x + 3 \cdot - 4 \frac{2}{3} = 64 (\frac{2}{3})$

Step 2.2.9.3

Rewrite the expression.

$8 x - 4 \cdot 2 = 64 (\frac{2}{3})$

Step 2.2.10

Multiply $- 4$ by $2$ .

$8 x - 8 = 64 (\frac{2}{3})$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply $64 (\frac{2}{3})$ .

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Step 2.3.1.1

Combine $64$ and $\frac{2}{3}$ .

$8 x - 8 = \frac{64 \cdot 2}{3}$

Step 2.3.1.2

Multiply $64$ by $2$ .

$8 x - 8 = \frac{128}{3}$

Step 3

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

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Step 3.1

Add $8$ to both sides of the equation.

$8 x = \frac{128}{3} + 8$

Step 3.2

To write $8$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$8 x = \frac{128}{3} + 8 \cdot \frac{3}{3}$

Step 3.3

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

$8 x = \frac{128}{3} + \frac{8 \cdot 3}{3}$

Step 3.4

Combine the numerators over the common denominator.

$8 x = \frac{128 + 8 \cdot 3}{3}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $8$ by $3$ .

$8 x = \frac{128 + 24}{3}$

Step 3.5.2

Add $128$ and $24$ .

$8 x = \frac{152}{3}$

Step 4

Divide each term in $8 x = \frac{152}{3}$ by $8$ and simplify.

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Step 4.1

Divide each term in $8 x = \frac{152}{3}$ by $8$ .

$\frac{8 x}{8} = \frac{\frac{152}{3}}{8}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $8$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{\frac{152}{3}}{8}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{152}{3}}{8}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{152}{3} \cdot \frac{1}{8}$

Step 4.3.2

Cancel the common factor of $8$ .

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Step 4.3.2.1

Factor $8$ out of $152$ .

$x = \frac{8 (19)}{3} \cdot \frac{1}{8}$

Step 4.3.2.2

Cancel the common factor.

$x = \frac{8 \cdot 19}{3} \cdot \frac{1}{8}$

Step 4.3.2.3

Rewrite the expression.

$x = \frac{19}{3}$