Solve 1/4(3-2x)-2>1/3x

$$\frac { 1 } { 4 } ( 3 - 2 x ) - 2 > \frac { 1 } { 3 } x$$

Solve for x

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

Solution Steps

Use the distributive property to multiply \frac{1}{4} by 3-2x.

$$\frac{1}{4}\times 3+\frac{1}{4}\left(-2\right)x-2>\frac{1}{3}x$$

Multiply \frac{1}{4} and 3 to get \frac{3}{4}.

$$\frac{3}{4}+\frac{1}{4}\left(-2\right)x-2>\frac{1}{3}x$$

Multiply \frac{1}{4} and -2 to get \frac{-2}{4}.

$$\frac{3}{4}+\frac{-2}{4}x-2>\frac{1}{3}x$$

Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{3}{4}-\frac{1}{2}x-2>\frac{1}{3}x$$

Convert 2 to fraction \frac{8}{4}.

$$\frac{3}{4}-\frac{1}{2}x-\frac{8}{4}>\frac{1}{3}x$$

Since \frac{3}{4} and \frac{8}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-8}{4}-\frac{1}{2}x>\frac{1}{3}x$$

Subtract 8 from 3 to get -5.

$$-\frac{5}{4}-\frac{1}{2}x>\frac{1}{3}x$$

Subtract \frac{1}{3}x from both sides.

$$-\frac{5}{4}-\frac{1}{2}x-\frac{1}{3}x>0$$

Combine -\frac{1}{2}x and -\frac{1}{3}x to get -\frac{5}{6}x.

$$-\frac{5}{4}-\frac{5}{6}x>0$$

Add \frac{5}{4} to both sides. Anything plus zero gives itself.

$$-\frac{5}{6}x>\frac{5}{4}$$

Multiply both sides by -\frac{6}{5}, the reciprocal of -\frac{5}{6}. Since -\frac{5}{6} is negative, the inequality direction is changed.

$$x<\frac{5}{4}\left(-\frac{6}{5}\right)$$

Multiply \frac{5}{4} times -\frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$x<\frac{5\left(-6\right)}{4\times 5}$$

Cancel out 5 in both numerator and denominator.

$$x<\frac{-6}{4}$$

Reduce the fraction \frac{-6}{4} to lowest terms by extracting and canceling out 2.

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