Solve 5-2x/3>x

$$\frac { 5 - 2 x } { 3 } > x$$

Solve for x

$$x<1$$

Solution Steps

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

$$\frac{5}{3}-\frac{2}{3}x>x$$

Subtract x from both sides.

$$\frac{5}{3}-\frac{2}{3}x-x>0$$

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

$$\frac{5}{3}-\frac{5}{3}x>0$$

Subtract \frac{5}{3} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{5}{3}x>-\frac{5}{3}$$

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

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

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

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

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

$$x<\frac{15}{15}$$

Divide 15 by 15 to get 1.

$$x<1$$