Pre-Algebra Examples

$- \frac{3 x}{4} + 1 = \frac{5}{12}$

Step 1

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

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Step 1.1

Subtract $1$ from both sides of the equation.

$- \frac{3 x}{4} = \frac{5}{12} - 1$

Step 1.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$- \frac{3 x}{4} = \frac{5}{12} - 1 \cdot \frac{12}{12}$

Step 1.3

Combine $- 1$ and $\frac{12}{12}$ .

$- \frac{3 x}{4} = \frac{5}{12} + \frac{- 1 \cdot 12}{12}$

Step 1.4

Combine the numerators over the common denominator.

$- \frac{3 x}{4} = \frac{5 - 1 \cdot 12}{12}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $- 1$ by $12$ .

$- \frac{3 x}{4} = \frac{5 - 12}{12}$

Step 1.5.2

Subtract $12$ from $5$ .

$- \frac{3 x}{4} = \frac{- 7}{12}$

Step 1.6

Move the negative in front of the fraction.

$- \frac{3 x}{4} = - \frac{7}{12}$

Step 2

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

$- \frac{4}{3} (- \frac{3 x}{4}) = - \frac{4}{3} (- \frac{7}{12})$

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 $- \frac{4}{3} (- \frac{3 x}{4})$ .

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Step 3.1.1.1

Cancel the common factor of $4$ .

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Step 3.1.1.1.1

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$\frac{- 4}{3} (- \frac{3 x}{4}) = - \frac{4}{3} (- \frac{7}{12})$

Step 3.1.1.1.2

Move the leading negative in $- \frac{3 x}{4}$ into the numerator.

$\frac{- 4}{3} \cdot \frac{- 3 x}{4} = - \frac{4}{3} (- \frac{7}{12})$

Step 3.1.1.1.3

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{3} \cdot \frac{- 3 x}{4} = - \frac{4}{3} (- \frac{7}{12})$

Step 3.1.1.1.4

Cancel the common factor.

$\frac{4 \cdot - 1}{3} \cdot \frac{- 3 x}{4} = - \frac{4}{3} (- \frac{7}{12})$

Step 3.1.1.1.5

Rewrite the expression.

$\frac{- 1}{3} (- 3 x) = - \frac{4}{3} (- \frac{7}{12})$

Step 3.1.1.2

Cancel the common factor of $3$ .

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Step 3.1.1.2.1

Factor $3$ out of $- 3 x$ .

$\frac{- 1}{3} (3 (- x)) = - \frac{4}{3} (- \frac{7}{12})$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{- 1}{3} (3 (- x)) = - \frac{4}{3} (- \frac{7}{12})$

Step 3.1.1.2.3

Rewrite the expression.

$- - x = - \frac{4}{3} (- \frac{7}{12})$

Step 3.1.1.3

Multiply.

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Step 3.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{4}{3} (- \frac{7}{12})$

Step 3.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{4}{3} (- \frac{7}{12})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $- \frac{4}{3} (- \frac{7}{12})$ .

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Step 3.2.1.1

Cancel the common factor of $4$ .

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Step 3.2.1.1.1

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$x = \frac{- 4}{3} (- \frac{7}{12})$

Step 3.2.1.1.2

Move the leading negative in $- \frac{7}{12}$ into the numerator.

$x = \frac{- 4}{3} \cdot \frac{- 7}{12}$

Step 3.2.1.1.3

Factor $4$ out of $- 4$ .

$x = \frac{4 (- 1)}{3} \cdot \frac{- 7}{12}$

Step 3.2.1.1.4

Factor $4$ out of $12$ .

$x = \frac{4 \cdot - 1}{3} \cdot \frac{- 7}{4 \cdot 3}$

Step 3.2.1.1.5

Cancel the common factor.

$x = \frac{4 \cdot - 1}{3} \cdot \frac{- 7}{4 \cdot 3}$

Step 3.2.1.1.6

Rewrite the expression.

$x = \frac{- 1}{3} \cdot \frac{- 7}{3}$

Step 3.2.1.2

Multiply $\frac{- 1}{3}$ by $\frac{- 7}{3}$ .

$x = \frac{- - 7}{3 \cdot 3}$

Step 3.2.1.3

Multiply.

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Step 3.2.1.3.1

Multiply $- 1$ by $- 7$ .

$x = \frac{7}{3 \cdot 3}$

Step 3.2.1.3.2

Multiply $3$ by $3$ .

$x = \frac{7}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{9}$

Decimal Form:

$x = 0.\overline{7}$