Solve for x 5/6-(x+5)/42=1

$\frac{5}{6} - \frac{x + 5}{42} = 1$

Simplify $\frac{5}{6} - \frac{x + 5}{42}$ .

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

$\frac{5}{6} \cdot \frac{7}{7} - \frac{x + 5}{42} = 1$

Write each expression with a common denominator of $42$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{6}$ by $\frac{7}{7}$ .

$\frac{5 \cdot 7}{6 \cdot 7} - \frac{x + 5}{42} = 1$

Multiply $6$ by $7$ .

$\frac{5 \cdot 7}{42} - \frac{x + 5}{42} = 1$

Combine the numerators over the common denominator.

$\frac{5 \cdot 7 - (x + 5)}{42} = 1$

Simplify the numerator.

Multiply $5$ by $7$ .

$\frac{35 - (x + 5)}{42} = 1$

Apply the distributive property.

$\frac{35 - x - 1 \cdot 5}{42} = 1$

Multiply $- 1$ by $5$ .

$\frac{35 - x - 5}{42} = 1$

Subtract $5$ from $35$ .

$\frac{- x + 30}{42} = 1$

Simplify with factoring out.

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

$\frac{- (x) + 30}{42} = 1$

Rewrite $30$ as $- 1 (- 30)$ .

$\frac{- (x) - 1 (- 30)}{42} = 1$

Factor $- 1$ out of $- (x) - 1 (- 30)$ .

$\frac{- (x - 30)}{42} = 1$

Simplify the expression.

Rewrite $- (x - 30)$ as $- 1 (x - 30)$ .

$\frac{- 1 (x - 30)}{42} = 1$

Move the negative in front of the fraction.

$- \frac{x - 30}{42} = 1$

Multiply both sides of the equation by $- 42$ .

$- 42 (- \frac{x - 30}{42}) = - 42 \cdot 1$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 42 (- \frac{x - 30}{42})$ .

Cancel the common factor of $42$ .

Move the leading negative in $- \frac{x - 30}{42}$ into the numerator.

$- 42 \frac{- (x - 30)}{42} = - 42 \cdot 1$

Factor $42$ out of $- 42$ .

$42 (- 1) \frac{- (x - 30)}{42} = - 42 \cdot 1$

Cancel the common factor.

$42 \cdot - 1 \frac{- (x - 30)}{42} = - 42 \cdot 1$

Rewrite the expression.

$- - (x - 30) = - 42 \cdot 1$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (x - 30) = - 42 \cdot 1$

Multiply $x - 30$ by $1$ .

$x - 30 = - 42 \cdot 1$

Simplify the right side.

Multiply $- 42$ by $1$ .

$x - 30 = - 42$

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

Add $30$ to both sides of the equation.

$x = - 42 + 30$

Add $- 42$ and $30$ .

$x = - 12$

Solve for x 5/6-(x+5)/42=1

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