Algebra Examples

$- \frac{5}{6} \cdot (9 + 2 x) = 40$

Step 1

Multiply both sides of the equation by $- \frac{6}{5}$ .

$- \frac{6}{5} (- \frac{5}{6} \cdot (9 + 2 x)) = - \frac{6}{5} \cdot 40$

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 $- \frac{6}{5} (- \frac{5}{6} \cdot (9 + 2 x))$ .

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Step 2.1.1.1

Simplify terms.

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Step 2.1.1.1.1

Apply the distributive property.

$- \frac{6}{5} (- \frac{5}{6} \cdot 9 - \frac{5}{6} (2 x)) = - \frac{6}{5} \cdot 40$

Step 2.1.1.1.2

Cancel the common factor of $3$ .

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Step 2.1.1.1.2.1

Move the leading negative in $- \frac{5}{6}$ into the numerator.

$- \frac{6}{5} (\frac{- 5}{6} \cdot 9 - \frac{5}{6} (2 x)) = - \frac{6}{5} \cdot 40$

Step 2.1.1.1.2.2

Factor $3$ out of $6$ .

$- \frac{6}{5} (\frac{- 5}{3 (2)} \cdot 9 - \frac{5}{6} (2 x)) = - \frac{6}{5} \cdot 40$

Step 2.1.1.1.2.3

Factor $3$ out of $9$ .

$- \frac{6}{5} (\frac{- 5}{3 \cdot 2} \cdot (3 \cdot 3) - \frac{5}{6} (2 x)) = - \frac{6}{5} \cdot 40$

Step 2.1.1.1.2.4

Cancel the common factor.

$- \frac{6}{5} (\frac{- 5}{3 \cdot 2} \cdot (3 \cdot 3) - \frac{5}{6} (2 x)) = - \frac{6}{5} \cdot 40$

Step 2.1.1.1.2.5

Rewrite the expression.

$- \frac{6}{5} (\frac{- 5}{2} \cdot 3 - \frac{5}{6} (2 x)) = - \frac{6}{5} \cdot 40$

Step 2.1.1.1.3

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

$- \frac{6}{5} (\frac{- 5 \cdot 3}{2} - \frac{5}{6} (2 x)) = - \frac{6}{5} \cdot 40$

Step 2.1.1.1.4

Multiply $- 5$ by $3$ .

$- \frac{6}{5} (\frac{- 15}{2} - \frac{5}{6} (2 x)) = - \frac{6}{5} \cdot 40$

Step 2.1.1.1.5

Cancel the common factor of $2$ .

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Step 2.1.1.1.5.1

Move the leading negative in $- \frac{5}{6}$ into the numerator.

$- \frac{6}{5} (\frac{- 15}{2} + \frac{- 5}{6} (2 x)) = - \frac{6}{5} \cdot 40$

Step 2.1.1.1.5.2

Factor $2$ out of $6$ .

$- \frac{6}{5} (\frac{- 15}{2} + \frac{- 5}{2 (3)} (2 x)) = - \frac{6}{5} \cdot 40$

Step 2.1.1.1.5.3

Factor $2$ out of $2 x$ .

$- \frac{6}{5} (\frac{- 15}{2} + \frac{- 5}{2 (3)} (2 (x))) = - \frac{6}{5} \cdot 40$

Step 2.1.1.1.5.4

Cancel the common factor.

$- \frac{6}{5} (\frac{- 15}{2} + \frac{- 5}{2 \cdot 3} (2 x)) = - \frac{6}{5} \cdot 40$

Step 2.1.1.1.5.5

Rewrite the expression.

$- \frac{6}{5} (\frac{- 15}{2} + \frac{- 5}{3} x) = - \frac{6}{5} \cdot 40$

Step 2.1.1.1.6

Combine $\frac{- 5}{3}$ and $x$ .

$- \frac{6}{5} (\frac{- 15}{2} + \frac{- 5 x}{3}) = - \frac{6}{5} \cdot 40$

Step 2.1.1.2

Simplify each term.

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Step 2.1.1.2.1

Move the negative in front of the fraction.

$- \frac{6}{5} (- \frac{15}{2} + \frac{- 5 x}{3}) = - \frac{6}{5} \cdot 40$

Step 2.1.1.2.2

Move the negative in front of the fraction.

$- \frac{6}{5} (- \frac{15}{2} - \frac{5 x}{3}) = - \frac{6}{5} \cdot 40$

Step 2.1.1.3

Simplify terms.

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Step 2.1.1.3.1

Apply the distributive property.

$- \frac{6}{5} (- \frac{15}{2}) - \frac{6}{5} (- \frac{5 x}{3}) = - \frac{6}{5} \cdot 40$

Step 2.1.1.3.2

Cancel the common factor of $2$ .

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Step 2.1.1.3.2.1

Move the leading negative in $- \frac{6}{5}$ into the numerator.

$\frac{- 6}{5} (- \frac{15}{2}) - \frac{6}{5} (- \frac{5 x}{3}) = - \frac{6}{5} \cdot 40$

Step 2.1.1.3.2.2

Move the leading negative in $- \frac{15}{2}$ into the numerator.

$\frac{- 6}{5} \cdot \frac{- 15}{2} - \frac{6}{5} (- \frac{5 x}{3}) = - \frac{6}{5} \cdot 40$

Step 2.1.1.3.2.3

Factor $2$ out of $- 6$ .

$\frac{2 (- 3)}{5} \cdot \frac{- 15}{2} - \frac{6}{5} (- \frac{5 x}{3}) = - \frac{6}{5} \cdot 40$

Step 2.1.1.3.2.4

Cancel the common factor.

$\frac{2 \cdot - 3}{5} \cdot \frac{- 15}{2} - \frac{6}{5} (- \frac{5 x}{3}) = - \frac{6}{5} \cdot 40$

Step 2.1.1.3.2.5

Rewrite the expression.

$\frac{- 3}{5} \cdot - 15 - \frac{6}{5} (- \frac{5 x}{3}) = - \frac{6}{5} \cdot 40$

Step 2.1.1.3.3

Cancel the common factor of $5$ .

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Step 2.1.1.3.3.1

Factor $5$ out of $- 15$ .

$\frac{- 3}{5} \cdot (5 (- 3)) - \frac{6}{5} (- \frac{5 x}{3}) = - \frac{6}{5} \cdot 40$

Step 2.1.1.3.3.2

Cancel the common factor.

$\frac{- 3}{5} \cdot (5 \cdot - 3) - \frac{6}{5} (- \frac{5 x}{3}) = - \frac{6}{5} \cdot 40$

Step 2.1.1.3.3.3

Rewrite the expression.

$- 3 \cdot - 3 - \frac{6}{5} (- \frac{5 x}{3}) = - \frac{6}{5} \cdot 40$

Step 2.1.1.3.4

Multiply $- 3$ by $- 3$ .

$9 - \frac{6}{5} (- \frac{5 x}{3}) = - \frac{6}{5} \cdot 40$

Step 2.1.1.3.5

Cancel the common factor of $3$ .

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Step 2.1.1.3.5.1

Move the leading negative in $- \frac{6}{5}$ into the numerator.

$9 + \frac{- 6}{5} (- \frac{5 x}{3}) = - \frac{6}{5} \cdot 40$

Step 2.1.1.3.5.2

Move the leading negative in $- \frac{5 x}{3}$ into the numerator.

$9 + \frac{- 6}{5} \cdot \frac{- 5 x}{3} = - \frac{6}{5} \cdot 40$

Step 2.1.1.3.5.3

Factor $3$ out of $- 6$ .

$9 + \frac{3 (- 2)}{5} \cdot \frac{- 5 x}{3} = - \frac{6}{5} \cdot 40$

Step 2.1.1.3.5.4

Cancel the common factor.

$9 + \frac{3 \cdot - 2}{5} \cdot \frac{- 5 x}{3} = - \frac{6}{5} \cdot 40$

Step 2.1.1.3.5.5

Rewrite the expression.

$9 + \frac{- 2}{5} (- 5 x) = - \frac{6}{5} \cdot 40$

Step 2.1.1.3.6

Cancel the common factor of $5$ .

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Step 2.1.1.3.6.1

Factor $5$ out of $- 5 x$ .

$9 + \frac{- 2}{5} (5 (- x)) = - \frac{6}{5} \cdot 40$

Step 2.1.1.3.6.2

Cancel the common factor.

$9 + \frac{- 2}{5} (5 (- x)) = - \frac{6}{5} \cdot 40$

Step 2.1.1.3.6.3

Rewrite the expression.

$9 - 2 (- x) = - \frac{6}{5} \cdot 40$

Step 2.1.1.3.7

Multiply $- 1$ by $- 2$ .

$9 + 2 x = - \frac{6}{5} \cdot 40$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $- \frac{6}{5} \cdot 40$ .

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Step 2.2.1.1

Cancel the common factor of $5$ .

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Step 2.2.1.1.1

Move the leading negative in $- \frac{6}{5}$ into the numerator.

$9 + 2 x = \frac{- 6}{5} \cdot 40$

Step 2.2.1.1.2

Factor $5$ out of $40$ .

$9 + 2 x = \frac{- 6}{5} \cdot (5 (8))$

Step 2.2.1.1.3

Cancel the common factor.

$9 + 2 x = \frac{- 6}{5} \cdot (5 \cdot 8)$

Step 2.2.1.1.4

Rewrite the expression.

$9 + 2 x = - 6 \cdot 8$

Step 2.2.1.2

Multiply $- 6$ by $8$ .

$9 + 2 x = - 48$

Step 3

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

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Step 3.1

Subtract $9$ from both sides of the equation.

$2 x = - 48 - 9$

Step 3.2

Subtract $9$ from $- 48$ .

$2 x = - 57$

Step 4

Divide each term in $2 x = - 57$ by $2$ and simplify.

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Step 4.1

Divide each term in $2 x = - 57$ by $2$ .

$\frac{2 x}{2} = \frac{- 57}{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 57}{2}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 57}{2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

$x = - \frac{57}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{57}{2}$

Decimal Form:

$x = - 28.5$

Mixed Number Form:

$x = - 28 \frac{1}{2}$