Solve 8(5-x)=4/5(x+13)

$$8 ( 5 - x ) = \frac { 4 } { 5 } ( x + 13 )$$

Solve for x

$$x = \frac{37}{11} = 3\frac{4}{11} \approx 3.363636364$$

Steps for Solving Linear Equation

Use the distributive property to multiply 8 by 5-x.

$$40-8x=\frac{4}{5}\left(x+13\right)$$

Use the distributive property to multiply \frac{4}{5} by x+13.

$$40-8x=\frac{4}{5}x+\frac{4}{5}\times 13$$

Express \frac{4}{5}\times 13 as a single fraction.

$$40-8x=\frac{4}{5}x+\frac{4\times 13}{5}$$

Multiply 4 and 13 to get 52.

$$40-8x=\frac{4}{5}x+\frac{52}{5}$$

Subtract \frac{4}{5}x from both sides.

$$40-8x-\frac{4}{5}x=\frac{52}{5}$$

Combine -8x and -\frac{4}{5}x to get -\frac{44}{5}x.

$$40-\frac{44}{5}x=\frac{52}{5}$$

Subtract 40 from both sides.

$$-\frac{44}{5}x=\frac{52}{5}-40$$

Convert 40 to fraction \frac{200}{5}.

$$-\frac{44}{5}x=\frac{52}{5}-\frac{200}{5}$$

Since \frac{52}{5} and \frac{200}{5} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{44}{5}x=\frac{52-200}{5}$$

Subtract 200 from 52 to get -148.

$$-\frac{44}{5}x=-\frac{148}{5}$$

Multiply both sides by -\frac{5}{44}, the reciprocal of -\frac{44}{5}.

$$x=-\frac{148}{5}\left(-\frac{5}{44}\right)$$

Multiply -\frac{148}{5} times -\frac{5}{44} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-148\left(-5\right)}{5\times 44}$$

Do the multiplications in the fraction \frac{-148\left(-5\right)}{5\times 44}.

$$x=\frac{740}{220}$$

Reduce the fraction \frac{740}{220} to lowest terms by extracting and canceling out 20.

$$x=\frac{37}{11}$$