Solve 18-1/3(24-x)-x<x

$$18- \frac{ 1 }{ 3 } (24-x)-x < x$$

Solve for x

$$x>6$$

Solution Steps

Use the distributive property to multiply -\frac{1}{3} by 24-x.

$$18-\frac{1}{3}\times 24-\frac{1}{3}\left(-1\right)x-x<x$$

Express -\frac{1}{3}\times 24 as a single fraction.

$$18+\frac{-24}{3}-\frac{1}{3}\left(-1\right)x-x<x$$

Divide -24 by 3 to get -8.

$$18-8-\frac{1}{3}\left(-1\right)x-x<x$$

Multiply -\frac{1}{3} and -1 to get \frac{1}{3}.

$$18-8+\frac{1}{3}x-x<x$$

Subtract 8 from 18 to get 10.

$$10+\frac{1}{3}x-x<x$$

Combine \frac{1}{3}x and -x to get -\frac{2}{3}x.

$$10-\frac{2}{3}x<x$$

Subtract x from both sides.

$$10-\frac{2}{3}x-x<0$$

Combine -\frac{2}{3}x and -x to get -\frac{5}{3}x.

$$10-\frac{5}{3}x<0$$

Subtract 10 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{5}{3}x<-10$$

Multiply both sides by -\frac{3}{5}, the reciprocal of -\frac{5}{3}. Since -\frac{5}{3} is negative, the inequality direction is changed.

$$x>-10\left(-\frac{3}{5}\right)$$

Express -10\left(-\frac{3}{5}\right) as a single fraction.

$$x>\frac{-10\left(-3\right)}{5}$$

Multiply -10 and -3 to get 30.

$$x>\frac{30}{5}$$

Divide 30 by 5 to get 6.

$$x>6$$