Solve for x (x-3)/10+(x+1)/4=2x-5

$\frac{x - 3}{10} + \frac{x + 1}{4} = 2 x - 5$

Step 1

Simplify $\frac{x - 3}{10} + \frac{x + 1}{4}$ .

To write $\frac{x - 3}{10}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x - 3}{10} \cdot \frac{2}{2} + \frac{x + 1}{4} = 2 x - 5$

To write $\frac{x + 1}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{x - 3}{10} \cdot \frac{2}{2} + \frac{x + 1}{4} \cdot \frac{5}{5} = 2 x - 5$

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

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

$\frac{(x - 3) \cdot 2}{10 \cdot 2} + \frac{x + 1}{4} \cdot \frac{5}{5} = 2 x - 5$

Multiply $10$ by $2$ .

$\frac{(x - 3) \cdot 2}{20} + \frac{x + 1}{4} \cdot \frac{5}{5} = 2 x - 5$

Multiply $\frac{x + 1}{4}$ by $\frac{5}{5}$ .

$\frac{(x - 3) \cdot 2}{20} + \frac{(x + 1) \cdot 5}{4 \cdot 5} = 2 x - 5$

Multiply $4$ by $5$ .

$\frac{(x - 3) \cdot 2}{20} + \frac{(x + 1) \cdot 5}{20} = 2 x - 5$

Combine the numerators over the common denominator.

$\frac{(x - 3) \cdot 2 + (x + 1) \cdot 5}{20} = 2 x - 5$

Simplify the numerator.

Apply the distributive property.

$\frac{x \cdot 2 - 3 \cdot 2 + (x + 1) \cdot 5}{20} = 2 x - 5$

Move $2$ to the left of $x$ .

$\frac{2 \cdot x - 3 \cdot 2 + (x + 1) \cdot 5}{20} = 2 x - 5$

Multiply $- 3$ by $2$ .

$\frac{2 \cdot x - 6 + (x + 1) \cdot 5}{20} = 2 x - 5$

Apply the distributive property.

$\frac{2 x - 6 + x \cdot 5 + 1 \cdot 5}{20} = 2 x - 5$

Move $5$ to the left of $x$ .

$\frac{2 x - 6 + 5 \cdot x + 1 \cdot 5}{20} = 2 x - 5$

Multiply $5$ by $1$ .

$\frac{2 x - 6 + 5 \cdot x + 5}{20} = 2 x - 5$

Add $2 x$ and $5 x$ .

$\frac{7 x - 6 + 5}{20} = 2 x - 5$

Add $- 6$ and $5$ .

$\frac{7 x - 1}{20} = 2 x - 5$

Step 2

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

Subtract $2 x$ from both sides of the equation.

$\frac{7 x - 1}{20} - 2 x = - 5$

To write $- 2 x$ as a fraction with a common denominator, multiply by $\frac{20}{20}$ .

$\frac{7 x - 1}{20} - 2 x \cdot \frac{20}{20} = - 5$

Combine $- 2 x$ and $\frac{20}{20}$ .

$\frac{7 x - 1}{20} + \frac{- 2 x \cdot 20}{20} = - 5$

Combine the numerators over the common denominator.

$\frac{7 x - 1 - 2 x \cdot 20}{20} = - 5$

Simplify the numerator.

Multiply $20$ by $- 2$ .

$\frac{7 x - 1 - 40 x}{20} = - 5$

Subtract $40 x$ from $7 x$ .

$\frac{- 33 x - 1}{20} = - 5$

Factor $- 1$ out of $- 33 x$ .

$\frac{- (33 x) - 1}{20} = - 5$

Rewrite $- 1$ as $- 1 (1)$ .

$\frac{- (33 x) - 1 (1)}{20} = - 5$

Factor $- 1$ out of $- (33 x) - 1 (1)$ .

$\frac{- (33 x + 1)}{20} = - 5$

Rewrite $- (33 x + 1)$ as $- 1 (33 x + 1)$ .

$\frac{- 1 (33 x + 1)}{20} = - 5$

Move the negative in front of the fraction.

$- \frac{33 x + 1}{20} = - 5$

Step 3

Multiply both sides of the equation by $- 20$ .

$- 20 (- \frac{33 x + 1}{20}) = - 20 \cdot - 5$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 20 (- \frac{33 x + 1}{20})$ .

Cancel the common factor of $20$ .

Move the leading negative in $- \frac{33 x + 1}{20}$ into the numerator.

$- 20 \frac{- (33 x + 1)}{20} = - 20 \cdot - 5$

Factor $20$ out of $- 20$ .

$20 (- 1) \frac{- (33 x + 1)}{20} = - 20 \cdot - 5$

Cancel the common factor.

$20 \cdot - 1 \frac{- (33 x + 1)}{20} = - 20 \cdot - 5$

Rewrite the expression.

$- - (33 x + 1) = - 20 \cdot - 5$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (33 x + 1) = - 20 \cdot - 5$

Multiply $33 x + 1$ by $1$ .

$33 x + 1 = - 20 \cdot - 5$

Simplify the right side.

Multiply $- 20$ by $- 5$ .

$33 x + 1 = 100$

Step 5

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

Subtract $1$ from both sides of the equation.

$33 x = 100 - 1$

Subtract $1$ from $100$ .

$33 x = 99$

Step 6

Divide each term in $33 x = 99$ by $33$ and simplify.

Divide each term in $33 x = 99$ by $33$ .

$\frac{33 x}{33} = \frac{99}{33}$

Simplify the left side.

Cancel the common factor of $33$ .

Cancel the common factor.

$\frac{33 x}{33} = \frac{99}{33}$

Divide $x$ by $1$ .

$x = \frac{99}{33}$

Simplify the right side.

Divide $99$ by $33$ .

$x = 3$

Solve for x (x-3)/10+(x+1)/4=2x-5

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