Solve 9/5x+12/5(40-x)-9=79.8

$$\frac{ 9 }{ 5 } x+ \frac{ 12 }{ 5 } (40-x)-9=79.8$$

Solve for x

$$x=12$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{12}{5} by 40-x.

$$\frac{9}{5}x+\frac{12}{5}\times 40+\frac{12}{5}\left(-1\right)x-9=79.8$$

Express \frac{12}{5}\times 40 as a single fraction.

$$\frac{9}{5}x+\frac{12\times 40}{5}+\frac{12}{5}\left(-1\right)x-9=79.8$$

Multiply 12 and 40 to get 480.

$$\frac{9}{5}x+\frac{480}{5}+\frac{12}{5}\left(-1\right)x-9=79.8$$

Divide 480 by 5 to get 96.

$$\frac{9}{5}x+96+\frac{12}{5}\left(-1\right)x-9=79.8$$

Multiply \frac{12}{5} and -1 to get -\frac{12}{5}.

$$\frac{9}{5}x+96-\frac{12}{5}x-9=79.8$$

Combine \frac{9}{5}x and -\frac{12}{5}x to get -\frac{3}{5}x.

$$-\frac{3}{5}x+96-9=79.8$$

Subtract 9 from 96 to get 87.

$$-\frac{3}{5}x+87=79.8$$

Subtract 87 from both sides.

$$-\frac{3}{5}x=79.8-87$$

Subtract 87 from 79.8 to get -7.2.

$$-\frac{3}{5}x=-7.2$$

Multiply both sides by -\frac{5}{3}, the reciprocal of -\frac{3}{5}.

$$x=-7.2\left(-\frac{5}{3}\right)$$

Convert decimal number -7.2 to fraction -\frac{72}{10}. Reduce the fraction -\frac{72}{10} to lowest terms by extracting and canceling out 2.

$$x=-\frac{36}{5}\left(-\frac{5}{3}\right)$$

Multiply -\frac{36}{5} times -\frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-36\left(-5\right)}{5\times 3}$$

Do the multiplications in the fraction \frac{-36\left(-5\right)}{5\times 3}.

$$x=\frac{180}{15}$$

Divide 180 by 15 to get 12.

$$x=12$$