Solve left(2-1/3xright)-3+4left(-1/2x+7/4right)>0

$$\left( 2- \frac{ 1 }{ 3 } x \right) -3+4 \left( - \frac{ 1 }{ 2 } x+ \frac{ 7 }{ 4 } \right) > 0$$

Solve for x

$$x<\frac{18}{7}$$

Solution Steps

Subtract 3 from 2 to get -1.

$$-1-\frac{1}{3}x+4\left(-\frac{1}{2}x+\frac{7}{4}\right)>0$$

Use the distributive property to multiply 4 by -\frac{1}{2}x+\frac{7}{4}.

$$-1-\frac{1}{3}x+4\left(-\frac{1}{2}\right)x+4\times \frac{7}{4}>0$$

Express 4\left(-\frac{1}{2}\right) as a single fraction.

$$-1-\frac{1}{3}x+\frac{4\left(-1\right)}{2}x+4\times \frac{7}{4}>0$$

Multiply 4 and -1 to get -4.

$$-1-\frac{1}{3}x+\frac{-4}{2}x+4\times \frac{7}{4}>0$$

Divide -4 by 2 to get -2.

$$-1-\frac{1}{3}x-2x+4\times \frac{7}{4}>0$$

Cancel out 4 and 4.

$$-1-\frac{1}{3}x-2x+7>0$$

Combine -\frac{1}{3}x and -2x to get -\frac{7}{3}x.

$$-1-\frac{7}{3}x+7>0$$

Add -1 and 7 to get 6.

$$6-\frac{7}{3}x>0$$

Subtract 6 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{7}{3}x>-6$$

Multiply both sides by -\frac{3}{7}, the reciprocal of -\frac{7}{3}. Since -\frac{7}{3} is negative, the inequality direction is changed.

$$x<-6\left(-\frac{3}{7}\right)$$

Express -6\left(-\frac{3}{7}\right) as a single fraction.

$$x<\frac{-6\left(-3\right)}{7}$$

Multiply -6 and -3 to get 18.

$$x<\frac{18}{7}$$