Algebra Examples

$\frac{2 x - 30}{5} + \frac{3 x - 55}{4} = \frac{22 x - 70}{20}$

Step 1

Cancel the common factor of $22 x - 70$ and $20$ .

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Step 1.1

Factor $2$ out of $22 x$ .

$\frac{2 x - 30}{5} + \frac{3 x - 55}{4} = \frac{2 (11 x) - 70}{20}$

Step 1.2

Factor $2$ out of $- 70$ .

$\frac{2 x - 30}{5} + \frac{3 x - 55}{4} = \frac{2 (11 x) + 2 (- 35)}{20}$

Step 1.3

Factor $2$ out of $2 (11 x) + 2 (- 35)$ .

$\frac{2 x - 30}{5} + \frac{3 x - 55}{4} = \frac{2 (11 x - 35)}{20}$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $2$ out of $20$ .

$\frac{2 x - 30}{5} + \frac{3 x - 55}{4} = \frac{2 (11 x - 35)}{2 (10)}$

Step 1.4.2

Cancel the common factor.

$\frac{2 x - 30}{5} + \frac{3 x - 55}{4} = \frac{2 (11 x - 35)}{2 \cdot 10}$

Step 1.4.3

Rewrite the expression.

$\frac{2 x - 30}{5} + \frac{3 x - 55}{4} = \frac{11 x - 35}{10}$

Step 2

Multiply both sides by $10$ .

$(\frac{2 x - 30}{5} + \frac{3 x - 55}{4}) \cdot 10 = \frac{11 x - 35}{10} \cdot 10$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $(\frac{2 x - 30}{5} + \frac{3 x - 55}{4}) \cdot 10$ .

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Step 3.1.1.1

Factor $2$ out of $2 x - 30$ .

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Step 3.1.1.1.1

Factor $2$ out of $2 x$ .

$(\frac{2 (x) - 30}{5} + \frac{3 x - 55}{4}) \cdot 10 = \frac{11 x - 35}{10} \cdot 10$

Step 3.1.1.1.2

Factor $2$ out of $- 30$ .

$(\frac{2 x + 2 \cdot - 15}{5} + \frac{3 x - 55}{4}) \cdot 10 = \frac{11 x - 35}{10} \cdot 10$

Step 3.1.1.1.3

Factor $2$ out of $2 x + 2 \cdot - 15$ .

$(\frac{2 (x - 15)}{5} + \frac{3 x - 55}{4}) \cdot 10 = \frac{11 x - 35}{10} \cdot 10$

Step 3.1.1.2

To write $\frac{2 (x - 15)}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(\frac{2 (x - 15)}{5} \cdot \frac{4}{4} + \frac{3 x - 55}{4}) \cdot 10 = \frac{11 x - 35}{10} \cdot 10$

Step 3.1.1.3

To write $\frac{3 x - 55}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(\frac{2 (x - 15)}{5} \cdot \frac{4}{4} + \frac{3 x - 55}{4} \cdot \frac{5}{5}) \cdot 10 = \frac{11 x - 35}{10} \cdot 10$

Step 3.1.1.4

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1.1.4.1

Multiply $\frac{2 (x - 15)}{5}$ by $\frac{4}{4}$ .

$(\frac{2 (x - 15) \cdot 4}{5 \cdot 4} + \frac{3 x - 55}{4} \cdot \frac{5}{5}) \cdot 10 = \frac{11 x - 35}{10} \cdot 10$

Step 3.1.1.4.2

Multiply $5$ by $4$ .

$(\frac{2 (x - 15) \cdot 4}{20} + \frac{3 x - 55}{4} \cdot \frac{5}{5}) \cdot 10 = \frac{11 x - 35}{10} \cdot 10$

Step 3.1.1.4.3

Multiply $\frac{3 x - 55}{4}$ by $\frac{5}{5}$ .

$(\frac{2 (x - 15) \cdot 4}{20} + \frac{(3 x - 55) \cdot 5}{4 \cdot 5}) \cdot 10 = \frac{11 x - 35}{10} \cdot 10$

Step 3.1.1.4.4

Multiply $4$ by $5$ .

$(\frac{2 (x - 15) \cdot 4}{20} + \frac{(3 x - 55) \cdot 5}{20}) \cdot 10 = \frac{11 x - 35}{10} \cdot 10$

Step 3.1.1.5

Combine the numerators over the common denominator.

$\frac{2 (x - 15) \cdot 4 + (3 x - 55) \cdot 5}{20} \cdot 10 = \frac{11 x - 35}{10} \cdot 10$

Step 3.1.1.6

Simplify the numerator.

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Step 3.1.1.6.1

Apply the distributive property.

$\frac{(2 x + 2 \cdot - 15) \cdot 4 + (3 x - 55) \cdot 5}{20} \cdot 10 = \frac{11 x - 35}{10} \cdot 10$

Step 3.1.1.6.2

Multiply $2$ by $- 15$ .

$\frac{(2 x - 30) \cdot 4 + (3 x - 55) \cdot 5}{20} \cdot 10 = \frac{11 x - 35}{10} \cdot 10$

Step 3.1.1.6.3

Apply the distributive property.

$\frac{2 x \cdot 4 - 30 \cdot 4 + (3 x - 55) \cdot 5}{20} \cdot 10 = \frac{11 x - 35}{10} \cdot 10$

Step 3.1.1.6.4

Multiply $4$ by $2$ .

$\frac{8 x - 30 \cdot 4 + (3 x - 55) \cdot 5}{20} \cdot 10 = \frac{11 x - 35}{10} \cdot 10$

Step 3.1.1.6.5

Multiply $- 30$ by $4$ .

$\frac{8 x - 120 + (3 x - 55) \cdot 5}{20} \cdot 10 = \frac{11 x - 35}{10} \cdot 10$

Step 3.1.1.6.6

Apply the distributive property.

$\frac{8 x - 120 + 3 x \cdot 5 - 55 \cdot 5}{20} \cdot 10 = \frac{11 x - 35}{10} \cdot 10$

Step 3.1.1.6.7

Multiply $5$ by $3$ .

$\frac{8 x - 120 + 15 x - 55 \cdot 5}{20} \cdot 10 = \frac{11 x - 35}{10} \cdot 10$

Step 3.1.1.6.8

Multiply $- 55$ by $5$ .

$\frac{8 x - 120 + 15 x - 275}{20} \cdot 10 = \frac{11 x - 35}{10} \cdot 10$

Step 3.1.1.6.9

Add $8 x$ and $15 x$ .

$\frac{23 x - 120 - 275}{20} \cdot 10 = \frac{11 x - 35}{10} \cdot 10$

Step 3.1.1.6.10

Subtract $275$ from $- 120$ .

$\frac{23 x - 395}{20} \cdot 10 = \frac{11 x - 35}{10} \cdot 10$

Step 3.1.1.7

Cancel the common factor of $10$ .

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Step 3.1.1.7.1

Factor $10$ out of $20$ .

$\frac{23 x - 395}{10 (2)} \cdot 10 = \frac{11 x - 35}{10} \cdot 10$

Step 3.1.1.7.2

Cancel the common factor.

$\frac{23 x - 395}{10 \cdot 2} \cdot 10 = \frac{11 x - 35}{10} \cdot 10$

Step 3.1.1.7.3

Rewrite the expression.

$\frac{23 x - 395}{2} = \frac{11 x - 35}{10} \cdot 10$

Step 3.2

Simplify the right 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.

$\frac{23 x - 395}{2} = \frac{11 x - 35}{10} \cdot 10$

Step 3.2.1.2

Rewrite the expression.

$\frac{23 x - 395}{2} = 11 x - 35$

Step 4

Solve for $x$ .

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Step 4.1

Multiply both sides by $2$ .

$\frac{23 x - 395}{2} \cdot 2 = (11 x - 35) \cdot 2$

Step 4.2

Simplify.

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.1.1.1

Cancel the common factor.

$\frac{23 x - 395}{2} \cdot 2 = (11 x - 35) \cdot 2$

Step 4.2.1.1.2

Rewrite the expression.

$23 x - 395 = (11 x - 35) \cdot 2$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Simplify $(11 x - 35) \cdot 2$ .

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Step 4.2.2.1.1

Apply the distributive property.

$23 x - 395 = 11 x \cdot 2 - 35 \cdot 2$

Step 4.2.2.1.2

Multiply.

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Step 4.2.2.1.2.1

Multiply $2$ by $11$ .

$23 x - 395 = 22 x - 35 \cdot 2$

Step 4.2.2.1.2.2

Multiply $- 35$ by $2$ .

$23 x - 395 = 22 x - 70$

Step 4.3

Solve for $x$ .

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Step 4.3.1

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

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Step 4.3.1.1

Subtract $22 x$ from both sides of the equation.

$23 x - 395 - 22 x = - 70$

Step 4.3.1.2

Subtract $22 x$ from $23 x$ .

$x - 395 = - 70$

Step 4.3.2

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

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Step 4.3.2.1

Add $395$ to both sides of the equation.

$x = - 70 + 395$

Step 4.3.2.2

Add $- 70$ and $395$ .

$x = 325$