Pre-Algebra Examples

$2 x + 40 = \frac{2}{11} x$

Step 1

Simplify $\frac{2}{11} x$ .

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Step 1.1

Rewrite.

$2 x + 40 = 0 + 0 + \frac{2}{11} x$

Step 1.2

Simplify by adding zeros.

$2 x + 40 = \frac{2}{11} x$

Step 1.3

Combine $\frac{2}{11}$ and $x$ .

$2 x + 40 = \frac{2 x}{11}$

Step 2

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

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Step 2.1

Subtract $\frac{2 x}{11}$ from both sides of the equation.

$2 x + 40 - \frac{2 x}{11} = 0$

Step 2.2

To write $2 x$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$2 x \cdot \frac{11}{11} - \frac{2 x}{11} + 40 = 0$

Step 2.3

Combine $2 x$ and $\frac{11}{11}$ .

$\frac{2 x \cdot 11}{11} - \frac{2 x}{11} + 40 = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{2 x \cdot 11 - 2 x}{11} + 40 = 0$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Factor $2 x$ out of $2 x \cdot 11 - 2 x$ .

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Step 2.5.1.1

Factor $2 x$ out of $2 x \cdot 11$ .

$\frac{2 x (11) - 2 x}{11} + 40 = 0$

Step 2.5.1.2

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

$\frac{2 x (11) + 2 x (- 1)}{11} + 40 = 0$

Step 2.5.1.3

Factor $2 x$ out of $2 x (11) + 2 x (- 1)$ .

$\frac{2 x (11 - 1)}{11} + 40 = 0$

Step 2.5.2

Subtract $1$ from $11$ .

$\frac{2 x \cdot 10}{11} + 40 = 0$

Step 2.5.3

Multiply $10$ by $2$ .

$\frac{20 x}{11} + 40 = 0$

Step 3

Subtract $40$ from both sides of the equation.

$\frac{20 x}{11} = - 40$

Step 4

Multiply both sides of the equation by $\frac{11}{20}$ .

$\frac{11}{20} \cdot \frac{20 x}{11} = \frac{11}{20} \cdot - 40$

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 $\frac{11}{20} \cdot \frac{20 x}{11}$ .

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Step 5.1.1.1

Cancel the common factor of $11$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{11}{20} \cdot \frac{20 x}{11} = \frac{11}{20} \cdot - 40$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{20} (20 x) = \frac{11}{20} \cdot - 40$

Step 5.1.1.2

Cancel the common factor of $20$ .

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Step 5.1.1.2.1

Factor $20$ out of $20 x$ .

$\frac{1}{20} (20 (x)) = \frac{11}{20} \cdot - 40$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{20} (20 x) = \frac{11}{20} \cdot - 40$

Step 5.1.1.2.3

Rewrite the expression.

$x = \frac{11}{20} \cdot - 40$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{11}{20} \cdot - 40$ .

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Step 5.2.1.1

Cancel the common factor of $20$ .

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Step 5.2.1.1.1

Factor $20$ out of $- 40$ .

$x = \frac{11}{20} \cdot (20 (- 2))$

Step 5.2.1.1.2

Cancel the common factor.

$x = \frac{11}{20} \cdot (20 \cdot - 2)$

Step 5.2.1.1.3

Rewrite the expression.

$x = 11 \cdot - 2$

Step 5.2.1.2

Multiply $11$ by $- 2$ .

$x = - 22$