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

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

Solve for x

$$x<-\frac{15}{7}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

Subtract 8 from 3 to get -5.

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

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

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

Combine -\frac{1}{4}x and -\frac{1}{3}x to get -\frac{7}{12}x.

$$-\frac{5}{4}-\frac{7}{12}x>0$$

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

$$-\frac{7}{12}x>\frac{5}{4}$$

Multiply both sides by -\frac{12}{7}, the reciprocal of -\frac{7}{12}. Since -\frac{7}{12} is negative, the inequality direction is changed.

$$x<\frac{5}{4}\left(-\frac{12}{7}\right)$$

Multiply \frac{5}{4} times -\frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$x<\frac{5\left(-12\right)}{4\times 7}$$

Do the multiplications in the fraction \frac{5\left(-12\right)}{4\times 7}.

$$x<\frac{-60}{28}$$

Reduce the fraction \frac{-60}{28} to lowest terms by extracting and canceling out 4.

$$x<-\frac{15}{7}$$