Pre-Algebra Examples

- 10 = \frac{2}{11} x

$- 10 = \frac{2}{11} x$

Step 1

Rewrite the equation as

\frac{2}{11} x = - 10

$\frac{2}{11} x = - 10$ .

\frac{2}{11} x = - 10

$\frac{2}{11} x = - 10$

Step 2

Multiply both sides of the equation by

\frac{11}{2}

$\frac{11}{2}$ .

\frac{11}{2} (\frac{2}{11} x) = \frac{11}{2} \cdot - 10

$\frac{11}{2} (\frac{2}{11} x) = \frac{11}{2} \cdot - 10$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify

\frac{11}{2} (\frac{2}{11} x)

$\frac{11}{2} (\frac{2}{11} x)$ .

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Step 3.1.1.1

Combine

\frac{2}{11}

$\frac{2}{11}$ and

x

$x$ .

\frac{11}{2} \cdot \frac{2 x}{11} = \frac{11}{2} \cdot - 10

$\frac{11}{2} \cdot \frac{2 x}{11} = \frac{11}{2} \cdot - 10$

Step 3.1.1.2

Cancel the common factor of

11

$11$ .

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Step 3.1.1.2.1

Cancel the common factor.

$\frac{11}{2} \cdot \frac{2 x}{11} = \frac{11}{2} \cdot - 10$

Step 3.1.1.2.2

Rewrite the expression.

$\frac{1}{2} (2 x) = \frac{11}{2} \cdot - 10$

Step 3.1.1.3

Cancel the common factor of

$2$ .

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Step 3.1.1.3.1

Factor

$2$ out of

$2 x$ .

$\frac{1}{2} (2 (x)) = \frac{11}{2} \cdot - 10$

Step 3.1.1.3.2

Cancel the common factor.

$\frac{1}{2} (2 x) = \frac{11}{2} \cdot - 10$

Step 3.1.1.3.3

Rewrite the expression.

$x = \frac{11}{2} \cdot - 10$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify

$\frac{11}{2} \cdot - 10$ .

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Step 3.2.1.1

Cancel the common factor of

$2$ .

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Step 3.2.1.1.1

Factor

$2$ out of

$- 10$ .

$x = \frac{11}{2} \cdot (2 (- 5))$

Step 3.2.1.1.2

Cancel the common factor.

$x = \frac{11}{2} \cdot (2 \cdot - 5)$

Step 3.2.1.1.3

Rewrite the expression.

$x = 11 \cdot - 5$

Step 3.2.1.2

Multiply

$11$ by

$- 5$ .

$x = - 55$