Solve for x (3x-9)/40-(x+3)/8=-1

$\frac{3 x - 9}{40} - \frac{x + 3}{8} = - 1$

Step 1

Simplify $\frac{3 x - 9}{40} - \frac{x + 3}{8}$ .

Factor $3$ out of $3 x - 9$ .

Factor $3$ out of $3 x$ .

$\frac{3 (x) - 9}{40} - \frac{x + 3}{8} = - 1$

Factor $3$ out of $- 9$ .

$\frac{3 x + 3 \cdot - 3}{40} - \frac{x + 3}{8} = - 1$

Factor $3$ out of $3 x + 3 \cdot - 3$ .

$\frac{3 (x - 3)}{40} - \frac{x + 3}{8} = - 1$

To write $- \frac{x + 3}{8}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3 (x - 3)}{40} - \frac{x + 3}{8} \cdot \frac{5}{5} = - 1$

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x + 3}{8}$ by $\frac{5}{5}$ .

$\frac{3 (x - 3)}{40} - \frac{(x + 3) \cdot 5}{8 \cdot 5} = - 1$

Multiply $8$ by $5$ .

$\frac{3 (x - 3)}{40} - \frac{(x + 3) \cdot 5}{40} = - 1$

Combine the numerators over the common denominator.

$\frac{3 (x - 3) - (x + 3) \cdot 5}{40} = - 1$

Simplify the numerator.

Apply the distributive property.

$\frac{3 x + 3 \cdot - 3 - (x + 3) \cdot 5}{40} = - 1$

Multiply $3$ by $- 3$ .

$\frac{3 x - 9 - (x + 3) \cdot 5}{40} = - 1$

Apply the distributive property.

$\frac{3 x - 9 + (- x - 1 \cdot 3) \cdot 5}{40} = - 1$

Multiply $- 1$ by $3$ .

$\frac{3 x - 9 + (- x - 3) \cdot 5}{40} = - 1$

Apply the distributive property.

$\frac{3 x - 9 - x \cdot 5 - 3 \cdot 5}{40} = - 1$

Multiply $5$ by $- 1$ .

$\frac{3 x - 9 - 5 x - 3 \cdot 5}{40} = - 1$

Multiply $- 3$ by $5$ .

$\frac{3 x - 9 - 5 x - 15}{40} = - 1$

Subtract $5 x$ from $3 x$ .

$\frac{- 2 x - 9 - 15}{40} = - 1$

Subtract $15$ from $- 9$ .

$\frac{- 2 x - 24}{40} = - 1$

Factor $2$ out of $- 2 x - 24$ .

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

$\frac{2 (- x) - 24}{40} = - 1$

Factor $2$ out of $- 24$ .

$\frac{2 (- x) + 2 (- 12)}{40} = - 1$

Factor $2$ out of $2 (- x) + 2 (- 12)$ .

$\frac{2 (- x - 12)}{40} = - 1$

Cancel the common factors.

Factor $2$ out of $40$ .

$\frac{2 (- x - 12)}{2 \cdot 20} = - 1$

Cancel the common factor.

$\frac{2 (- x - 12)}{2 \cdot 20} = - 1$

Rewrite the expression.

$\frac{- x - 12}{20} = - 1$

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

$\frac{- (x) - 12}{20} = - 1$

Rewrite $- 12$ as $- 1 (12)$ .

$\frac{- (x) - 1 (12)}{20} = - 1$

Factor $- 1$ out of $- (x) - 1 (12)$ .

$\frac{- (x + 12)}{20} = - 1$

Simplify the expression.

Rewrite $- (x + 12)$ as $- 1 (x + 12)$ .

$\frac{- 1 (x + 12)}{20} = - 1$

Move the negative in front of the fraction.

$- \frac{x + 12}{20} = - 1$

Step 2

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

$- 20 (- \frac{x + 12}{20}) = - 20 \cdot - 1$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 20 (- \frac{x + 12}{20})$ .

Cancel the common factor of $20$ .

Move the leading negative in $- \frac{x + 12}{20}$ into the numerator.

$- 20 \frac{- (x + 12)}{20} = - 20 \cdot - 1$

Factor $20$ out of $- 20$ .

$20 (- 1) \frac{- (x + 12)}{20} = - 20 \cdot - 1$

Cancel the common factor.

$20 \cdot - 1 \frac{- (x + 12)}{20} = - 20 \cdot - 1$

Rewrite the expression.

$- - (x + 12) = - 20 \cdot - 1$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (x + 12) = - 20 \cdot - 1$

Multiply $x + 12$ by $1$ .

$x + 12 = - 20 \cdot - 1$

Simplify the right side.

Multiply $- 20$ by $- 1$ .

$x + 12 = 20$

Step 4

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

Subtract $12$ from both sides of the equation.

$x = 20 - 12$

Subtract $12$ from $20$ .

$x = 8$

Solve for x (3x-9)/40-(x+3)/8=-1

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