Algebra Examples

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

Step 1

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

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Step 1.1

Rewrite.

$0 + 0 - \frac{3}{8} \cdot (x - 6) = 5 + 3 x$

Step 1.2

Simplify terms.

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Step 1.2.1

Apply the distributive property.

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

Step 1.2.2

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

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

Step 1.2.3

Cancel the common factor of $2$ .

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Step 1.2.3.1

Move the leading negative in $- \frac{3}{8}$ into the numerator.

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

Step 1.2.3.2

Factor $2$ out of $8$ .

$- \frac{x \cdot 3}{8} + \frac{- 3}{2 (4)} \cdot - 6 = 5 + 3 x$

Step 1.2.3.3

Factor $2$ out of $- 6$ .

$- \frac{x \cdot 3}{8} + \frac{- 3}{2 \cdot 4} \cdot (2 \cdot - 3) = 5 + 3 x$

Step 1.2.3.4

Cancel the common factor.

$- \frac{x \cdot 3}{8} + \frac{- 3}{2 \cdot 4} \cdot (2 \cdot - 3) = 5 + 3 x$

Step 1.2.3.5

Rewrite the expression.

$- \frac{x \cdot 3}{8} + \frac{- 3}{4} \cdot - 3 = 5 + 3 x$

Step 1.2.4

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

$- \frac{x \cdot 3}{8} + \frac{- 3 \cdot - 3}{4} = 5 + 3 x$

Step 1.2.5

Multiply $- 3$ by $- 3$ .

$- \frac{x \cdot 3}{8} + \frac{9}{4} = 5 + 3 x$

Step 1.3

Move $3$ to the left of $x$ .

$- \frac{3 x}{8} + \frac{9}{4} = 5 + 3 x$

Step 2

Move all terms containing $x$ to the left side of the equation.

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Step 2.1

Subtract $3 x$ from both sides of the equation.

$- \frac{3 x}{8} + \frac{9}{4} - 3 x = 5$

Step 2.2

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

$- \frac{3 x}{8} - 3 x \cdot \frac{8}{8} + \frac{9}{4} = 5$

Step 2.3

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

$- \frac{3 x}{8} + \frac{- 3 x \cdot 8}{8} + \frac{9}{4} = 5$

Step 2.4

Combine the numerators over the common denominator.

$\frac{- 3 x - 3 x \cdot 8}{8} + \frac{9}{4} = 5$

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

Factor $3 x$ out of $- 3 x - 3 x \cdot 8$ .

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Step 2.5.1.1.1

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

$\frac{3 x (- 1) - 3 x \cdot 8}{8} + \frac{9}{4} = 5$

Step 2.5.1.1.2

Factor $3 x$ out of $- 3 x \cdot 8$ .

$\frac{3 x (- 1) + 3 x (- 1 \cdot 8)}{8} + \frac{9}{4} = 5$

Step 2.5.1.1.3

Factor $3 x$ out of $3 x (- 1) + 3 x (- 1 \cdot 8)$ .

$\frac{3 x (- 1 - 1 \cdot 8)}{8} + \frac{9}{4} = 5$

Step 2.5.1.2

Multiply $- 1$ by $8$ .

$\frac{3 x (- 1 - 8)}{8} + \frac{9}{4} = 5$

Step 2.5.1.3

Subtract $8$ from $- 1$ .

$\frac{3 x \cdot - 9}{8} + \frac{9}{4} = 5$

Step 2.5.1.4

Multiply $- 9$ by $3$ .

$\frac{- 27 x}{8} + \frac{9}{4} = 5$

Step 2.5.2

Move the negative in front of the fraction.

$- \frac{27 x}{8} + \frac{9}{4} = 5$

Step 3

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

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Step 3.1

Subtract $\frac{9}{4}$ from both sides of the equation.

$- \frac{27 x}{8} = 5 - \frac{9}{4}$

Step 3.2

To write $5$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{27 x}{8} = 5 \cdot \frac{4}{4} - \frac{9}{4}$

Step 3.3

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

$- \frac{27 x}{8} = \frac{5 \cdot 4}{4} - \frac{9}{4}$

Step 3.4

Combine the numerators over the common denominator.

$- \frac{27 x}{8} = \frac{5 \cdot 4 - 9}{4}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $5$ by $4$ .

$- \frac{27 x}{8} = \frac{20 - 9}{4}$

Step 3.5.2

Subtract $9$ from $20$ .

$- \frac{27 x}{8} = \frac{11}{4}$

Step 4

Multiply both sides of the equation by $- \frac{8}{27}$ .

$- \frac{8}{27} (- \frac{27 x}{8}) = - \frac{8}{27} \cdot \frac{11}{4}$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $- \frac{8}{27} (- \frac{27 x}{8})$ .

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Step 5.1.1.1

Cancel the common factor of $8$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{8}{27}$ into the numerator.

$\frac{- 8}{27} (- \frac{27 x}{8}) = - \frac{8}{27} \cdot \frac{11}{4}$

Step 5.1.1.1.2

Move the leading negative in $- \frac{27 x}{8}$ into the numerator.

$\frac{- 8}{27} \cdot \frac{- 27 x}{8} = - \frac{8}{27} \cdot \frac{11}{4}$

Step 5.1.1.1.3

Factor $8$ out of $- 8$ .

$\frac{8 (- 1)}{27} \cdot \frac{- 27 x}{8} = - \frac{8}{27} \cdot \frac{11}{4}$

Step 5.1.1.1.4

Cancel the common factor.

$\frac{8 \cdot - 1}{27} \cdot \frac{- 27 x}{8} = - \frac{8}{27} \cdot \frac{11}{4}$

Step 5.1.1.1.5

Rewrite the expression.

$\frac{- 1}{27} (- 27 x) = - \frac{8}{27} \cdot \frac{11}{4}$

Step 5.1.1.2

Cancel the common factor of $27$ .

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Step 5.1.1.2.1

Factor $27$ out of $- 27 x$ .

$\frac{- 1}{27} (27 (- x)) = - \frac{8}{27} \cdot \frac{11}{4}$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{- 1}{27} (27 (- x)) = - \frac{8}{27} \cdot \frac{11}{4}$

Step 5.1.1.2.3

Rewrite the expression.

$- - x = - \frac{8}{27} \cdot \frac{11}{4}$

Step 5.1.1.3

Multiply.

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Step 5.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{8}{27} \cdot \frac{11}{4}$

Step 5.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{8}{27} \cdot \frac{11}{4}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- \frac{8}{27} \cdot \frac{11}{4}$ .

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Step 5.2.1.1

Cancel the common factor of $4$ .

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Step 5.2.1.1.1

Move the leading negative in $- \frac{8}{27}$ into the numerator.

$x = \frac{- 8}{27} \cdot \frac{11}{4}$

Step 5.2.1.1.2

Factor $4$ out of $- 8$ .

$x = \frac{4 (- 2)}{27} \cdot \frac{11}{4}$

Step 5.2.1.1.3

Cancel the common factor.

$x = \frac{4 \cdot - 2}{27} \cdot \frac{11}{4}$

Step 5.2.1.1.4

Rewrite the expression.

$x = \frac{- 2}{27} \cdot 11$

Step 5.2.1.2

Combine $\frac{- 2}{27}$ and $11$ .

$x = \frac{- 2 \cdot 11}{27}$

Step 5.2.1.3

Simplify the expression.

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Step 5.2.1.3.1

Multiply $- 2$ by $11$ .

$x = \frac{- 22}{27}$

Step 5.2.1.3.2

Move the negative in front of the fraction.

$x = - \frac{22}{27}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{22}{27}$

Decimal Form:

$x = - 0.\overline{814}$