Algebra Examples

$\frac{3}{4} (- 4.2 - x) = 5$

Step 1

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

$\frac{4}{3} (\frac{3}{4} \cdot (- 4.2 - x)) = \frac{4}{3} \cdot 5$

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 $\frac{4}{3} (\frac{3}{4} \cdot (- 4.2 - x))$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{4}{3} (\frac{3}{4} \cdot - 4.2 + \frac{3}{4} (- x)) = \frac{4}{3} \cdot 5$

Step 2.1.1.2

Multiply $\frac{3}{4} \cdot - 4.2$ .

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Step 2.1.1.2.1

Combine $\frac{3}{4}$ and $- 4.2$ .

$\frac{4}{3} (\frac{3 \cdot - 4.2}{4} + \frac{3}{4} (- x)) = \frac{4}{3} \cdot 5$

Step 2.1.1.2.2

Multiply $3$ by $- 4.2$ .

$\frac{4}{3} (\frac{- 12.6}{4} + \frac{3}{4} (- x)) = \frac{4}{3} \cdot 5$

Step 2.1.1.3

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

$\frac{4}{3} (\frac{- 12.6}{4} - \frac{3 x}{4}) = \frac{4}{3} \cdot 5$

Step 2.1.1.4

Divide $- 12.6$ by $4$ .

$\frac{4}{3} (- 3.15 - \frac{3 x}{4}) = \frac{4}{3} \cdot 5$

Step 2.1.1.5

Apply the distributive property.

$\frac{4}{3} \cdot - 3.15 + \frac{4}{3} (- \frac{3 x}{4}) = \frac{4}{3} \cdot 5$

Step 2.1.1.6

Multiply $\frac{4}{3} \cdot - 3.15$ .

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Step 2.1.1.6.1

Combine $\frac{4}{3}$ and $- 3.15$ .

$\frac{4 \cdot - 3.15}{3} + \frac{4}{3} (- \frac{3 x}{4}) = \frac{4}{3} \cdot 5$

Step 2.1.1.6.2

Multiply $4$ by $- 3.15$ .

$\frac{- 12.6}{3} + \frac{4}{3} (- \frac{3 x}{4}) = \frac{4}{3} \cdot 5$

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 $- \frac{3 x}{4}$ into the numerator.

$\frac{- 12.6}{3} + \frac{4}{3} \cdot \frac{- 3 x}{4} = \frac{4}{3} \cdot 5$

Step 2.1.1.7.2

Cancel the common factor.

$\frac{- 12.6}{3} + \frac{4}{3} \cdot \frac{- 3 x}{4} = \frac{4}{3} \cdot 5$

Step 2.1.1.7.3

Rewrite the expression.

$\frac{- 12.6}{3} + \frac{1}{3} (- 3 x) = \frac{4}{3} \cdot 5$

Step 2.1.1.8

Cancel the common factor of $3$ .

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Step 2.1.1.8.1

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

$\frac{- 12.6}{3} + \frac{1}{3} (3 (- x)) = \frac{4}{3} \cdot 5$

Step 2.1.1.8.2

Cancel the common factor.

$\frac{- 12.6}{3} + \frac{1}{3} (3 (- x)) = \frac{4}{3} \cdot 5$

Step 2.1.1.8.3

Rewrite the expression.

$\frac{- 12.6}{3} - x = \frac{4}{3} \cdot 5$

Step 2.1.1.9

Divide $- 12.6$ by $3$ .

$- 4.2 - x = \frac{4}{3} \cdot 5$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $\frac{4}{3} \cdot 5$ .

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Step 2.2.1.1

Combine $\frac{4}{3}$ and $5$ .

$- 4.2 - x = \frac{4 \cdot 5}{3}$

Step 2.2.1.2

Multiply $4$ by $5$ .

$- 4.2 - x = \frac{20}{3}$

Step 3

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

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Step 3.1

Add $4.2$ to both sides of the equation.

$- x = \frac{20}{3} + 4.2$

Step 3.2

To write $4.2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- x = \frac{20}{3} + 4.2 \cdot \frac{3}{3}$

Step 3.3

Combine $4.2$ and $\frac{3}{3}$ .

$- x = \frac{20}{3} + \frac{4.2 \cdot 3}{3}$

Step 3.4

Combine the numerators over the common denominator.

$- x = \frac{20 + 4.2 \cdot 3}{3}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $4.2$ by $3$ .

$- x = \frac{20 + 12.6}{3}$

Step 3.5.2

Add $20$ and $12.6$ .

$- x = \frac{32.6}{3}$

Step 3.6

Divide $32.6$ by $3$ .

$- x = 10.8\overline{6}$

Step 4

Divide each term in $- x = 10.8\overline{6}$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- x = 10.8\overline{6}$ by $- 1$ .

$\frac{- x}{- 1} = \frac{10.8\overline{6}}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{10.8\overline{6}}{- 1}$

Step 4.2.2

Divide $x$ by $1$ .

$x = \frac{10.8\overline{6}}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $10.8\overline{6}$ by $- 1$ .

$x = - 10.8\overline{6}$