Solve 144/21.6=18x/18x+72

$$\frac { 144 } { 21.6 } = \frac { 18 x } { 18 x + 72 }$$

Solve for x

$$x = -\frac{80}{17} = -4\frac{12}{17} \approx -4.705882353$$

Steps for Solving Linear Equation

Variable x cannot be equal to -4 since division by zero is not defined. Multiply both sides of the equation by 18\left(x+4\right).

$$18\left(x+4\right)\times \frac{144}{21.6}=18x$$

Use the distributive property to multiply 18 by x+4.

$$\left(18x+72\right)\times \frac{144}{21.6}=18x$$

Expand \frac{144}{21.6} by multiplying both numerator and the denominator by 10.

$$\left(18x+72\right)\times \frac{1440}{216}=18x$$

Reduce the fraction \frac{1440}{216} to lowest terms by extracting and canceling out 72.

$$\left(18x+72\right)\times \frac{20}{3}=18x$$

Use the distributive property to multiply 18x+72 by \frac{20}{3}.

$$120x+480=18x$$

Subtract 18x from both sides.

$$120x+480-18x=0$$

Combine 120x and -18x to get 102x.

$$102x+480=0$$

Subtract 480 from both sides. Anything subtracted from zero gives its negation.

$$102x=-480$$

Divide both sides by 102.

$$x=\frac{-480}{102}$$

Reduce the fraction \frac{-480}{102} to lowest terms by extracting and canceling out 6.

$$x=-\frac{80}{17}$$