Solve (5+0.5x)div1.5<x

$$(5+0.5x) \div 1.5 < x$$

Solve for x

$$x>5$$

Solution Steps

Divide each term of 5+0.5x by 1.5 to get \frac{5}{1.5}+\frac{0.5x}{1.5}.

$$\frac{5}{1.5}+\frac{0.5x}{1.5}<x$$

Expand \frac{5}{1.5} by multiplying both numerator and the denominator by 10.

$$\frac{50}{15}+\frac{0.5x}{1.5}<x$$

Reduce the fraction \frac{50}{15} to lowest terms by extracting and canceling out 5.

$$\frac{10}{3}+\frac{0.5x}{1.5}<x$$

Divide 0.5x by 1.5 to get \frac{1}{3}x.

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

Subtract x from both sides.

$$\frac{10}{3}+\frac{1}{3}x-x<0$$

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

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

Subtract \frac{10}{3} from both sides. Anything subtracted from zero gives its negation.

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

Divide both sides by -\frac{2}{3}. Since -\frac{2}{3} is negative, the inequality direction is changed.

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

Express \frac{-\frac{10}{3}}{-\frac{2}{3}} as a single fraction.

$$x>\frac{-10}{3\left(-\frac{2}{3}\right)}$$

Multiply 3 and -\frac{2}{3} to get -2.

$$x>\frac{-10}{-2}$$

Divide -10 by -2 to get 5.

$$x>5$$