Algebra Examples

$\frac{1}{6} (2 x - 12 x) = 30$

Step 1

Multiply both sides of the equation by $6$ .

$6 (\frac{1}{6} \cdot (2 x - 12 x)) = 6 \cdot 30$

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 $6 (\frac{1}{6} \cdot (2 x - 12 x))$ .

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Step 2.1.1.1

Subtract $12 x$ from $2 x$ .

$6 (\frac{1}{6} \cdot (- 10 x)) = 6 \cdot 30$

Step 2.1.1.2

Cancel the common factor of $2$ .

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Step 2.1.1.2.1

Factor $2$ out of $6$ .

$6 (\frac{1}{2 (3)} \cdot (- 10 x)) = 6 \cdot 30$

Step 2.1.1.2.2

Factor $2$ out of $- 10 x$ .

$6 (\frac{1}{2 (3)} \cdot (2 (- 5 x))) = 6 \cdot 30$

Step 2.1.1.2.3

Cancel the common factor.

$6 (\frac{1}{2 \cdot 3} \cdot (2 (- 5 x))) = 6 \cdot 30$

Step 2.1.1.2.4

Rewrite the expression.

$6 (\frac{1}{3} \cdot (- 5 x)) = 6 \cdot 30$

$6 (\frac{1}{3} \cdot (- 5 x)) = 6 \cdot 30$

Step 2.1.1.3

Combine $- 5$ and $\frac{1}{3}$ .

$6 (\frac{- 5}{3} \cdot x) = 6 \cdot 30$

Step 2.1.1.4

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

$6 \frac{- 5 x}{3} = 6 \cdot 30$

Step 2.1.1.5

Cancel the common factor of $3$ .

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Step 2.1.1.5.1

Factor $3$ out of $6$ .

$3 (2) \frac{- 5 x}{3} = 6 \cdot 30$

Step 2.1.1.5.2

Cancel the common factor.

$3 \cdot 2 \frac{- 5 x}{3} = 6 \cdot 30$

Step 2.1.1.5.3

Rewrite the expression.

$2 (- 5 x) = 6 \cdot 30$

$2 (- 5 x) = 6 \cdot 30$

Step 2.1.1.6

Multiply $- 5$ by $2$ .

$- 10 x = 6 \cdot 30$

$- 10 x = 6 \cdot 30$

$- 10 x = 6 \cdot 30$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $6$ by $30$ .

$- 10 x = 180$

$- 10 x = 180$

$- 10 x = 180$

Step 3

Divide each term in $- 10 x = 180$ by $- 10$ and simplify.

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Step 3.1

Divide each term in $- 10 x = 180$ by $- 10$ .

$\frac{- 10 x}{- 10} = \frac{180}{- 10}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 10$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 10 x}{- 10} = \frac{180}{- 10}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{180}{- 10}$

$x = \frac{180}{- 10}$

$x = \frac{180}{- 10}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $180$ by $- 10$ .

$x = - 18$

$x = - 18$

$x = - 18$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$