Solve for x (2x-30)/5+(3x-55)/4=(22x-70)/20

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

Step 1

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

Factor $2$ out of $22 x$ .

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

Factor $2$ out of $- 70$ .

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

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

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

Cancel the common factors.

Factor $2$ out of $20$ .

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

Cancel the common factor.

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

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.

Simplify the left side.

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

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

Factor $2$ out of $2 x$ .

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

Factor $2$ out of $- 30$ .

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

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

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

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

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

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

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

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

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

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

Multiply $5$ by $4$ .

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

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

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

Multiply $4$ by $5$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $2$ by $- 15$ .

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

Apply the distributive property.

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

Multiply $4$ by $2$ .

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

Multiply $- 30$ by $4$ .

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

Apply the distributive property.

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

Multiply $5$ by $3$ .

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

Multiply $- 55$ by $5$ .

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

Add $8 x$ and $15 x$ .

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

Subtract $275$ from $- 120$ .

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

Cancel the common factor of $10$ .

Factor $10$ out of $20$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Cancel the common factor of $10$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Solve for $x$ .

Multiply both sides by $2$ .

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

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

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

Apply the distributive property.

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

Multiply.

Multiply $2$ by $11$ .

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

Multiply $- 35$ by $2$ .

$23 x - 395 = 22 x - 70$

Solve for $x$ .

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

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

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

Subtract $22 x$ from $23 x$ .

$x - 395 = - 70$

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

Add $395$ to both sides of the equation.

$x = - 70 + 395$

Add $- 70$ and $395$ .

$x = 325$

Solve for x (2x-30)/5+(3x-55)/4=(22x-70)/20

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