Solve for x -5(7-8x)=47

$- 5 (7 - 8 x) = 47$

Step 1

Divide each term in $- 5 (7 - 8 x) = 47$ by $- 5$ and simplify.

Divide each term in $- 5 (7 - 8 x) = 47$ by $- 5$ .

$\frac{- 5 (7 - 8 x)}{- 5} = \frac{47}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 (7 - 8 x)}{- 5} = \frac{47}{- 5}$

Divide $7 - 8 x$ by $1$ .

$7 - 8 x = \frac{47}{- 5}$

Simplify the right side.

Move the negative in front of the fraction.

$7 - 8 x = - \frac{47}{5}$

Step 2

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

Subtract $7$ from both sides of the equation.

$- 8 x = - \frac{47}{5} - 7$

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

$- 8 x = - \frac{47}{5} - 7 \cdot \frac{5}{5}$

Combine $- 7$ and $\frac{5}{5}$ .

$- 8 x = - \frac{47}{5} + \frac{- 7 \cdot 5}{5}$

Combine the numerators over the common denominator.

$- 8 x = \frac{- 47 - 7 \cdot 5}{5}$

Simplify the numerator.

Multiply $- 7$ by $5$ .

$- 8 x = \frac{- 47 - 35}{5}$

Subtract $35$ from $- 47$ .

$- 8 x = \frac{- 82}{5}$

Move the negative in front of the fraction.

$- 8 x = - \frac{82}{5}$

Step 3

Divide each term in $- 8 x = - \frac{82}{5}$ by $- 8$ and simplify.

Divide each term in $- 8 x = - \frac{82}{5}$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{- \frac{82}{5}}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{- \frac{82}{5}}{- 8}$

Divide $x$ by $1$ .

$x = \frac{- \frac{82}{5}}{- 8}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{82}{5} \cdot \frac{1}{- 8}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{82}{5}$ into the numerator.

$x = \frac{- 82}{5} \cdot \frac{1}{- 8}$

Factor $2$ out of $- 82$ .

$x = \frac{2 (- 41)}{5} \cdot \frac{1}{- 8}$

Factor $2$ out of $- 8$ .

$x = \frac{2 \cdot - 41}{5} \cdot \frac{1}{2 \cdot - 4}$

Cancel the common factor.

$x = \frac{2 \cdot - 41}{5} \cdot \frac{1}{2 \cdot - 4}$

Rewrite the expression.

$x = \frac{- 41}{5} \cdot \frac{1}{- 4}$

Multiply $\frac{- 41}{5}$ by $\frac{1}{- 4}$ .

$x = \frac{- 41}{5 \cdot - 4}$

Multiply $5$ by $- 4$ .

$x = \frac{- 41}{- 20}$

Dividing two negative values results in a positive value.

$x = \frac{41}{20}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{41}{20}$

Decimal Form:

$x = 2.05$

Mixed Number Form:

$x = 2 \frac{1}{20}$

Solve for x -5(7-8x)=47

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