Algebra Examples

$10 = \frac{4}{3} (8 x + 6)$

Step 1

Rewrite the equation as $\frac{4}{3} \cdot (8 x + 6) = 10$ .

$\frac{4}{3} \cdot (8 x + 6) = 10$

Step 2

Multiply both sides of the equation by $\frac{3}{4}$ .

$\frac{3}{4} (\frac{4}{3} \cdot (8 x + 6)) = \frac{3}{4} \cdot 10$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{3}{4} (\frac{4}{3} \cdot (8 x + 6))$ .

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Step 3.1.1.1

Apply the distributive property.

$\frac{3}{4} (\frac{4}{3} (8 x) + \frac{4}{3} \cdot 6) = \frac{3}{4} \cdot 10$

Step 3.1.1.2

Multiply $\frac{4}{3} (8 x)$ .

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Step 3.1.1.2.1

Combine $8$ and $\frac{4}{3}$ .

$\frac{3}{4} (\frac{8 \cdot 4}{3} x + \frac{4}{3} \cdot 6) = \frac{3}{4} \cdot 10$

Step 3.1.1.2.2

Multiply $8$ by $4$ .

$\frac{3}{4} (\frac{32}{3} x + \frac{4}{3} \cdot 6) = \frac{3}{4} \cdot 10$

Step 3.1.1.2.3

Combine $\frac{32}{3}$ and $x$ .

$\frac{3}{4} (\frac{32 x}{3} + \frac{4}{3} \cdot 6) = \frac{3}{4} \cdot 10$

Step 3.1.1.3

Cancel the common factor of $3$ .

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Step 3.1.1.3.1

Factor $3$ out of $6$ .

$\frac{3}{4} (\frac{32 x}{3} + \frac{4}{3} \cdot (3 (2))) = \frac{3}{4} \cdot 10$

Step 3.1.1.3.2

Cancel the common factor.

$\frac{3}{4} (\frac{32 x}{3} + \frac{4}{3} \cdot (3 \cdot 2)) = \frac{3}{4} \cdot 10$

Step 3.1.1.3.3

Rewrite the expression.

$\frac{3}{4} (\frac{32 x}{3} + 4 \cdot 2) = \frac{3}{4} \cdot 10$

Step 3.1.1.4

Multiply $4$ by $2$ .

$\frac{3}{4} (\frac{32 x}{3} + 8) = \frac{3}{4} \cdot 10$

Step 3.1.1.5

Apply the distributive property.

$\frac{3}{4} \cdot \frac{32 x}{3} + \frac{3}{4} \cdot 8 = \frac{3}{4} \cdot 10$

Step 3.1.1.6

Cancel the common factor of $3$ .

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Step 3.1.1.6.1

Cancel the common factor.

$\frac{3}{4} \cdot \frac{32 x}{3} + \frac{3}{4} \cdot 8 = \frac{3}{4} \cdot 10$

Step 3.1.1.6.2

Rewrite the expression.

$\frac{1}{4} (32 x) + \frac{3}{4} \cdot 8 = \frac{3}{4} \cdot 10$

Step 3.1.1.7

Cancel the common factor of $4$ .

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Step 3.1.1.7.1

Factor $4$ out of $32 x$ .

$\frac{1}{4} (4 (8 x)) + \frac{3}{4} \cdot 8 = \frac{3}{4} \cdot 10$

Step 3.1.1.7.2

Cancel the common factor.

$\frac{1}{4} (4 (8 x)) + \frac{3}{4} \cdot 8 = \frac{3}{4} \cdot 10$

Step 3.1.1.7.3

Rewrite the expression.

$8 x + \frac{3}{4} \cdot 8 = \frac{3}{4} \cdot 10$

Step 3.1.1.8

Cancel the common factor of $4$ .

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Step 3.1.1.8.1

Factor $4$ out of $8$ .

$8 x + \frac{3}{4} \cdot (4 (2)) = \frac{3}{4} \cdot 10$

Step 3.1.1.8.2

Cancel the common factor.

$8 x + \frac{3}{4} \cdot (4 \cdot 2) = \frac{3}{4} \cdot 10$

Step 3.1.1.8.3

Rewrite the expression.

$8 x + 3 \cdot 2 = \frac{3}{4} \cdot 10$

Step 3.1.1.9

Multiply $3$ by $2$ .

$8 x + 6 = \frac{3}{4} \cdot 10$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{3}{4} \cdot 10$ .

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Step 3.2.1.1

Cancel the common factor of $2$ .

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Step 3.2.1.1.1

Factor $2$ out of $4$ .

$8 x + 6 = \frac{3}{2 (2)} \cdot 10$

Step 3.2.1.1.2

Factor $2$ out of $10$ .

$8 x + 6 = \frac{3}{2 \cdot 2} \cdot (2 \cdot 5)$

Step 3.2.1.1.3

Cancel the common factor.

$8 x + 6 = \frac{3}{2 \cdot 2} \cdot (2 \cdot 5)$

Step 3.2.1.1.4

Rewrite the expression.

$8 x + 6 = \frac{3}{2} \cdot 5$

Step 3.2.1.2

Combine $\frac{3}{2}$ and $5$ .

$8 x + 6 = \frac{3 \cdot 5}{2}$

Step 3.2.1.3

Multiply $3$ by $5$ .

$8 x + 6 = \frac{15}{2}$

Step 4

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

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Step 4.1

Subtract $6$ from both sides of the equation.

$8 x = \frac{15}{2} - 6$

Step 4.2

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$8 x = \frac{15}{2} - 6 \cdot \frac{2}{2}$

Step 4.3

Combine $- 6$ and $\frac{2}{2}$ .

$8 x = \frac{15}{2} + \frac{- 6 \cdot 2}{2}$

Step 4.4

Combine the numerators over the common denominator.

$8 x = \frac{15 - 6 \cdot 2}{2}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 6$ by $2$ .

$8 x = \frac{15 - 12}{2}$

Step 4.5.2

Subtract $12$ from $15$ .

$8 x = \frac{3}{2}$

Step 5

Divide each term in $8 x = \frac{3}{2}$ by $8$ and simplify.

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Step 5.1

Divide each term in $8 x = \frac{3}{2}$ by $8$ .

$\frac{8 x}{8} = \frac{\frac{3}{2}}{8}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $8$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{\frac{3}{2}}{8}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{3}{2}}{8}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{3}{2} \cdot \frac{1}{8}$

Step 5.3.2

Multiply $\frac{3}{2} \cdot \frac{1}{8}$ .

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Step 5.3.2.1

Multiply $\frac{3}{2}$ by $\frac{1}{8}$ .

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

Step 5.3.2.2

Multiply $2$ by $8$ .

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.1875$