Solve for x (x+5)/5-(2x-12)/7=1

$\frac{x + 5}{5} - \frac{2 x - 12}{7} = 1$

Step 1

Simplify $\frac{x + 5}{5} - \frac{2 x - 12}{7}$ .

Factor $2$ out of $2 x - 12$ .

Factor $2$ out of $2 x$ .

$\frac{x + 5}{5} - \frac{2 (x) - 12}{7} = 1$

Factor $2$ out of $- 12$ .

$\frac{x + 5}{5} - \frac{2 x + 2 \cdot - 6}{7} = 1$

Factor $2$ out of $2 x + 2 \cdot - 6$ .

$\frac{x + 5}{5} - \frac{2 (x - 6)}{7} = 1$

To write $\frac{x + 5}{5}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{x + 5}{5} \cdot \frac{7}{7} - \frac{2 (x - 6)}{7} = 1$

To write $- \frac{2 (x - 6)}{7}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{x + 5}{5} \cdot \frac{7}{7} - \frac{2 (x - 6)}{7} \cdot \frac{5}{5} = 1$

Write each expression with a common denominator of $35$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x + 5}{5}$ by $\frac{7}{7}$ .

$\frac{(x + 5) \cdot 7}{5 \cdot 7} - \frac{2 (x - 6)}{7} \cdot \frac{5}{5} = 1$

Multiply $5$ by $7$ .

$\frac{(x + 5) \cdot 7}{35} - \frac{2 (x - 6)}{7} \cdot \frac{5}{5} = 1$

Multiply $\frac{2 (x - 6)}{7}$ by $\frac{5}{5}$ .

$\frac{(x + 5) \cdot 7}{35} - \frac{2 (x - 6) \cdot 5}{7 \cdot 5} = 1$

Multiply $7$ by $5$ .

$\frac{(x + 5) \cdot 7}{35} - \frac{2 (x - 6) \cdot 5}{35} = 1$

Combine the numerators over the common denominator.

$\frac{(x + 5) \cdot 7 - 2 (x - 6) \cdot 5}{35} = 1$

Simplify the numerator.

Apply the distributive property.

$\frac{x \cdot 7 + 5 \cdot 7 - 2 (x - 6) \cdot 5}{35} = 1$

Move $7$ to the left of $x$ .

$\frac{7 \cdot x + 5 \cdot 7 - 2 (x - 6) \cdot 5}{35} = 1$

Multiply $5$ by $7$ .

$\frac{7 \cdot x + 35 - 2 (x - 6) \cdot 5}{35} = 1$

Apply the distributive property.

$\frac{7 x + 35 + (- 2 x - 2 \cdot - 6) \cdot 5}{35} = 1$

Multiply $- 2$ by $- 6$ .

$\frac{7 x + 35 + (- 2 x + 12) \cdot 5}{35} = 1$

Apply the distributive property.

$\frac{7 x + 35 - 2 x \cdot 5 + 12 \cdot 5}{35} = 1$

Multiply $5$ by $- 2$ .

$\frac{7 x + 35 - 10 x + 12 \cdot 5}{35} = 1$

Multiply $12$ by $5$ .

$\frac{7 x + 35 - 10 x + 60}{35} = 1$

Subtract $10 x$ from $7 x$ .

$\frac{- 3 x + 35 + 60}{35} = 1$

Add $35$ and $60$ .

$\frac{- 3 x + 95}{35} = 1$

Simplify with factoring out.

Factor $- 1$ out of $- 3 x$ .

$\frac{- (3 x) + 95}{35} = 1$

Rewrite $95$ as $- 1 (- 95)$ .

$\frac{- (3 x) - 1 (- 95)}{35} = 1$

Factor $- 1$ out of $- (3 x) - 1 (- 95)$ .

$\frac{- (3 x - 95)}{35} = 1$

Simplify the expression.

Rewrite $- (3 x - 95)$ as $- 1 (3 x - 95)$ .

$\frac{- 1 (3 x - 95)}{35} = 1$

Move the negative in front of the fraction.

$- \frac{3 x - 95}{35} = 1$

Step 2

Multiply both sides of the equation by $- 35$ .

$- 35 (- \frac{3 x - 95}{35}) = - 35 \cdot 1$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 35 (- \frac{3 x - 95}{35})$ .

Cancel the common factor of $35$ .

Move the leading negative in $- \frac{3 x - 95}{35}$ into the numerator.

$- 35 \frac{- (3 x - 95)}{35} = - 35 \cdot 1$

Factor $35$ out of $- 35$ .

$35 (- 1) \frac{- (3 x - 95)}{35} = - 35 \cdot 1$

Cancel the common factor.

$35 \cdot - 1 \frac{- (3 x - 95)}{35} = - 35 \cdot 1$

Rewrite the expression.

$- - (3 x - 95) = - 35 \cdot 1$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (3 x - 95) = - 35 \cdot 1$

Multiply $3 x - 95$ by $1$ .

$3 x - 95 = - 35 \cdot 1$

Simplify the right side.

Multiply $- 35$ by $1$ .

$3 x - 95 = - 35$

Step 4

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

Add $95$ to both sides of the equation.

$3 x = - 35 + 95$

Add $- 35$ and $95$ .

$3 x = 60$

Step 5

Divide each term in $3 x = 60$ by $3$ and simplify.

Divide each term in $3 x = 60$ by $3$ .

$\frac{3 x}{3} = \frac{60}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{60}{3}$

Divide $x$ by $1$ .

$x = \frac{60}{3}$

Simplify the right side.

Divide $60$ by $3$ .

$x = 20$

Solve for x (x+5)/5-(2x-12)/7=1

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