Algebra Examples

$\frac{2 x}{5} + \frac{3 x}{2} - \frac{2 x}{3} = 37$

Step 1

Simplify $\frac{2 x}{5} + \frac{3 x}{2} - \frac{2 x}{3}$ .

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Step 1.1

Find the common denominator.

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Step 1.1.1

Multiply $\frac{2 x}{5}$ by $\frac{6}{6}$ .

$\frac{2 x}{5} \cdot \frac{6}{6} + \frac{3 x}{2} - \frac{2 x}{3} = 37$

Step 1.1.2

Multiply $\frac{2 x}{5}$ by $\frac{6}{6}$ .

$\frac{2 x \cdot 6}{5 \cdot 6} + \frac{3 x}{2} - \frac{2 x}{3} = 37$

Step 1.1.3

Multiply $\frac{3 x}{2}$ by $\frac{15}{15}$ .

$\frac{2 x \cdot 6}{5 \cdot 6} + \frac{3 x}{2} \cdot \frac{15}{15} - \frac{2 x}{3} = 37$

Step 1.1.4

Multiply $\frac{3 x}{2}$ by $\frac{15}{15}$ .

$\frac{2 x \cdot 6}{5 \cdot 6} + \frac{3 x \cdot 15}{2 \cdot 15} - \frac{2 x}{3} = 37$

Step 1.1.5

Multiply $\frac{2 x}{3}$ by $\frac{10}{10}$ .

$\frac{2 x \cdot 6}{5 \cdot 6} + \frac{3 x \cdot 15}{2 \cdot 15} - (\frac{2 x}{3} \cdot \frac{10}{10}) = 37$

Step 1.1.6

Multiply $\frac{2 x}{3}$ by $\frac{10}{10}$ .

$\frac{2 x \cdot 6}{5 \cdot 6} + \frac{3 x \cdot 15}{2 \cdot 15} - \frac{2 x \cdot 10}{3 \cdot 10} = 37$

Step 1.1.7

Multiply $5$ by $6$ .

$\frac{2 x \cdot 6}{30} + \frac{3 x \cdot 15}{2 \cdot 15} - \frac{2 x \cdot 10}{3 \cdot 10} = 37$

Step 1.1.8

Multiply $2$ by $15$ .

$\frac{2 x \cdot 6}{30} + \frac{3 x \cdot 15}{30} - \frac{2 x \cdot 10}{3 \cdot 10} = 37$

Step 1.1.9

Multiply $3$ by $10$ .

$\frac{2 x \cdot 6}{30} + \frac{3 x \cdot 15}{30} - \frac{2 x \cdot 10}{30} = 37$

Step 1.2

Combine the numerators over the common denominator.

$\frac{2 x \cdot 6 + 3 x \cdot 15 - 2 x \cdot 10}{30} = 37$

Step 1.3

Simplify each term.

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Step 1.3.1

Multiply $6$ by $2$ .

$\frac{12 x + 3 x \cdot 15 - 2 x \cdot 10}{30} = 37$

Step 1.3.2

Multiply $15$ by $3$ .

$\frac{12 x + 45 x - 2 x \cdot 10}{30} = 37$

Step 1.3.3

Multiply $10$ by $- 2$ .

$\frac{12 x + 45 x - 20 x}{30} = 37$

Step 1.4

Simplify by adding terms.

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Step 1.4.1

Add $12 x$ and $45 x$ .

$\frac{57 x - 20 x}{30} = 37$

Step 1.4.2

Subtract $20 x$ from $57 x$ .

$\frac{37 x}{30} = 37$

Step 2

Multiply both sides of the equation by $\frac{30}{37}$ .

$\frac{30}{37} \cdot \frac{37 x}{30} = \frac{30}{37} \cdot 37$

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 $\frac{30}{37} \cdot \frac{37 x}{30}$ .

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Step 3.1.1.1

Cancel the common factor of $30$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{30}{37} \cdot \frac{37 x}{30} = \frac{30}{37} \cdot 37$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{37} (37 x) = \frac{30}{37} \cdot 37$

Step 3.1.1.2

Cancel the common factor of $37$ .

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Step 3.1.1.2.1

Factor $37$ out of $37 x$ .

$\frac{1}{37} (37 (x)) = \frac{30}{37} \cdot 37$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{37} (37 x) = \frac{30}{37} \cdot 37$

Step 3.1.1.2.3

Rewrite the expression.

$x = \frac{30}{37} \cdot 37$

Step 3.2

Simplify the right side.

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Step 3.2.1

Cancel the common factor of $37$ .

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Step 3.2.1.1

Cancel the common factor.

$x = \frac{30}{37} \cdot 37$

Step 3.2.1.2

Rewrite the expression.

$x = 30$