Solve 1-2-5x/3<x

$$1- \frac{ 2-5x }{ 3 } < x$$

Solve for x

$$x<-\frac{1}{2}$$

Solution Steps

Divide each term of 2-5x by 3 to get \frac{2}{3}-\frac{5}{3}x.

$$1-\left(\frac{2}{3}-\frac{5}{3}x\right)<x$$

To find the opposite of \frac{2}{3}-\frac{5}{3}x, find the opposite of each term.

$$1-\frac{2}{3}-\left(-\frac{5}{3}x\right)<x$$

The opposite of -\frac{5}{3}x is \frac{5}{3}x.

$$1-\frac{2}{3}+\frac{5}{3}x<x$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{3}{3}-\frac{2}{3}+\frac{5}{3}x<x$$

Since \frac{3}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-2}{3}+\frac{5}{3}x<x$$

Subtract 2 from 3 to get 1.

$$\frac{1}{3}+\frac{5}{3}x<x$$

Subtract x from both sides.

$$\frac{1}{3}+\frac{5}{3}x-x<0$$

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

$$\frac{1}{3}+\frac{2}{3}x<0$$

Subtract \frac{1}{3} from both sides. Anything subtracted from zero gives its negation.

$$\frac{2}{3}x<-\frac{1}{3}$$

Multiply both sides by \frac{3}{2}, the reciprocal of \frac{2}{3}. Since \frac{2}{3} is positive, the inequality direction remains the same.

$$x<-\frac{1}{3}\times \frac{3}{2}$$

Multiply -\frac{1}{3} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 3 in both numerator and denominator.

$$x<\frac{-1}{2}$$

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$x<-\frac{1}{2}$$