Algebra Examples

$- \frac{3}{4} = \frac{3 x}{4} + \frac{11}{8}$

Step 1

Rewrite the equation as $\frac{3 x}{4} + \frac{11}{8} = - \frac{3}{4}$ .

$\frac{3 x}{4} + \frac{11}{8} = - \frac{3}{4}$

Step 2

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

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Step 2.1

Subtract $\frac{11}{8}$ from both sides of the equation.

$\frac{3 x}{4} = - \frac{3}{4} - \frac{11}{8}$

Step 2.2

To write $- \frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 x}{4} = - \frac{3}{4} \cdot \frac{2}{2} - \frac{11}{8}$

Step 2.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

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

$\frac{3 x}{4} = - \frac{3 \cdot 2}{4 \cdot 2} - \frac{11}{8}$

Step 2.3.2

Multiply $4$ by $2$ .

$\frac{3 x}{4} = - \frac{3 \cdot 2}{8} - \frac{11}{8}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{3 x}{4} = \frac{- 3 \cdot 2 - 11}{8}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 3$ by $2$ .

$\frac{3 x}{4} = \frac{- 6 - 11}{8}$

Step 2.5.2

Subtract $11$ from $- 6$ .

$\frac{3 x}{4} = \frac{- 17}{8}$

Step 2.6

Move the negative in front of the fraction.

$\frac{3 x}{4} = - \frac{17}{8}$

Step 3

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

$\frac{4}{3} \cdot \frac{3 x}{4} = \frac{4}{3} (- \frac{17}{8})$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

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

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Step 4.1.1.1

Cancel the common factor of $4$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{4}{3} \cdot \frac{3 x}{4} = \frac{4}{3} (- \frac{17}{8})$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 x) = \frac{4}{3} (- \frac{17}{8})$

Step 4.1.1.2

Cancel the common factor of $3$ .

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Step 4.1.1.2.1

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{4}{3} (- \frac{17}{8})$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{4}{3} (- \frac{17}{8})$

Step 4.1.1.2.3

Rewrite the expression.

$x = \frac{4}{3} (- \frac{17}{8})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{4}{3} (- \frac{17}{8})$ .

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Step 4.2.1.1

Cancel the common factor of $4$ .

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Step 4.2.1.1.1

Move the leading negative in $- \frac{17}{8}$ into the numerator.

$x = \frac{4}{3} \cdot \frac{- 17}{8}$

Step 4.2.1.1.2

Factor $4$ out of $8$ .

$x = \frac{4}{3} \cdot \frac{- 17}{4 (2)}$

Step 4.2.1.1.3

Cancel the common factor.

$x = \frac{4}{3} \cdot \frac{- 17}{4 \cdot 2}$

Step 4.2.1.1.4

Rewrite the expression.

$x = \frac{1}{3} \cdot \frac{- 17}{2}$

Step 4.2.1.2

Multiply $\frac{1}{3}$ by $\frac{- 17}{2}$ .

$x = \frac{- 17}{3 \cdot 2}$

Step 4.2.1.3

Simplify the expression.

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Step 4.2.1.3.1

Multiply $3$ by $2$ .

$x = \frac{- 17}{6}$

Step 4.2.1.3.2

Move the negative in front of the fraction.

$x = - \frac{17}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{17}{6}$

Decimal Form:

$x = - 2.8\overline{3}$

Mixed Number Form:

$x = - 2 \frac{5}{6}$