Algebra Examples

$\frac{4}{9} x - 12 = - \frac{1}{6} (x - 12) - 3$

Step 1

Combine $\frac{4}{9}$ and $x$ .

$\frac{4 x}{9} - 12 = - \frac{1}{6} \cdot (x - 12) - 3$

Step 2

Simplify $- \frac{1}{6} \cdot (x - 12) - 3$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$\frac{4 x}{9} - 12 = - \frac{1}{6} x - \frac{1}{6} \cdot - 12 - 3$

Step 2.1.2

Combine $x$ and $\frac{1}{6}$ .

$\frac{4 x}{9} - 12 = - \frac{x}{6} - \frac{1}{6} \cdot - 12 - 3$

Step 2.1.3

Cancel the common factor of $6$ .

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Step 2.1.3.1

Move the leading negative in $- \frac{1}{6}$ into the numerator.

$\frac{4 x}{9} - 12 = - \frac{x}{6} + \frac{- 1}{6} \cdot - 12 - 3$

Step 2.1.3.2

Factor $6$ out of $- 12$ .

$\frac{4 x}{9} - 12 = - \frac{x}{6} + \frac{- 1}{6} \cdot (6 (- 2)) - 3$

Step 2.1.3.3

Cancel the common factor.

$\frac{4 x}{9} - 12 = - \frac{x}{6} + \frac{- 1}{6} \cdot (6 \cdot - 2) - 3$

Step 2.1.3.4

Rewrite the expression.

$\frac{4 x}{9} - 12 = - \frac{x}{6} - 1 \cdot - 2 - 3$

Step 2.1.4

Multiply $- 1$ by $- 2$ .

$\frac{4 x}{9} - 12 = - \frac{x}{6} + 2 - 3$

Step 2.2

Subtract $3$ from $2$ .

$\frac{4 x}{9} - 12 = - \frac{x}{6} - 1$

Step 3

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

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Step 3.1

Add $\frac{x}{6}$ to both sides of the equation.

$\frac{4 x}{9} - 12 + \frac{x}{6} = - 1$

Step 3.2

To write $\frac{4 x}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{4 x}{9} \cdot \frac{2}{2} + \frac{x}{6} - 12 = - 1$

Step 3.3

To write $\frac{x}{6}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{4 x}{9} \cdot \frac{2}{2} + \frac{x}{6} \cdot \frac{3}{3} - 12 = - 1$

Step 3.4

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{4 x}{9}$ by $\frac{2}{2}$ .

$\frac{4 x \cdot 2}{9 \cdot 2} + \frac{x}{6} \cdot \frac{3}{3} - 12 = - 1$

Step 3.4.2

Multiply $9$ by $2$ .

$\frac{4 x \cdot 2}{18} + \frac{x}{6} \cdot \frac{3}{3} - 12 = - 1$

Step 3.4.3

Multiply $\frac{x}{6}$ by $\frac{3}{3}$ .

$\frac{4 x \cdot 2}{18} + \frac{x \cdot 3}{6 \cdot 3} - 12 = - 1$

Step 3.4.4

Multiply $6$ by $3$ .

$\frac{4 x \cdot 2}{18} + \frac{x \cdot 3}{18} - 12 = - 1$

Step 3.5

Combine the numerators over the common denominator.

$\frac{4 x \cdot 2 + x \cdot 3}{18} - 12 = - 1$

Step 3.6

Simplify each term.

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Step 3.6.1

Simplify the numerator.

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Step 3.6.1.1

Factor $x$ out of $4 x \cdot 2 + x \cdot 3$ .

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Step 3.6.1.1.1

Factor $x$ out of $4 x \cdot 2$ .

$\frac{x (4 \cdot 2) + x \cdot 3}{18} - 12 = - 1$

Step 3.6.1.1.2

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

$\frac{x (4 \cdot 2) + x (3)}{18} - 12 = - 1$

Step 3.6.1.1.3

Factor $x$ out of $x (4 \cdot 2) + x (3)$ .

$\frac{x (4 \cdot 2 + 3)}{18} - 12 = - 1$

Step 3.6.1.2

Multiply $4$ by $2$ .

$\frac{x (8 + 3)}{18} - 12 = - 1$

Step 3.6.1.3

Add $8$ and $3$ .

$\frac{x \cdot 11}{18} - 12 = - 1$

Step 3.6.2

Move $11$ to the left of $x$ .

$\frac{11 x}{18} - 12 = - 1$

Step 4

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

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Step 4.1

Add $12$ to both sides of the equation.

$\frac{11 x}{18} = - 1 + 12$

Step 4.2

Add $- 1$ and $12$ .

$\frac{11 x}{18} = 11$

Step 5

Multiply both sides of the equation by $\frac{18}{11}$ .

$\frac{18}{11} \cdot \frac{11 x}{18} = \frac{18}{11} \cdot 11$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $\frac{18}{11} \cdot \frac{11 x}{18}$ .

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Step 6.1.1.1

Cancel the common factor of $18$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{18}{11} \cdot \frac{11 x}{18} = \frac{18}{11} \cdot 11$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{11} (11 x) = \frac{18}{11} \cdot 11$

Step 6.1.1.2

Cancel the common factor of $11$ .

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Step 6.1.1.2.1

Factor $11$ out of $11 x$ .

$\frac{1}{11} (11 (x)) = \frac{18}{11} \cdot 11$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{11} (11 x) = \frac{18}{11} \cdot 11$

Step 6.1.1.2.3

Rewrite the expression.

$x = \frac{18}{11} \cdot 11$

Step 6.2

Simplify the right side.

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Step 6.2.1

Cancel the common factor of $11$ .

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Step 6.2.1.1

Cancel the common factor.

$x = \frac{18}{11} \cdot 11$

Step 6.2.1.2

Rewrite the expression.

$x = 18$