Solve 4/5x-21/2x-2<3-1/6-1/5x

$$\frac { 4 } { 5 } x - 2 \frac { 1 } { 2 } x - 2 < 3 - \frac { 1 } { 6 } - \frac { 1 } { 5 } x$$

Solve for x

$$x>-\frac{29}{9}$$

Solution Steps

Multiply both sides of the equation by 30, the least common multiple of 5,2,6. Since 30 is positive, the inequality direction remains the same.

$$30\left(\frac{4}{5}x-\frac{2\times 2+1}{2}x\right)-60<90-5-6x$$

Multiply 2 and 2 to get 4.

$$30\left(\frac{4}{5}x-\frac{4+1}{2}x\right)-60<90-5-6x$$

Add 4 and 1 to get 5.

$$30\left(\frac{4}{5}x-\frac{5}{2}x\right)-60<90-5-6x$$

Combine \frac{4}{5}x and -\frac{5}{2}x to get -\frac{17}{10}x.

$$30\left(-\frac{17}{10}\right)x-60<90-5-6x$$

Express 30\left(-\frac{17}{10}\right) as a single fraction.

$$\frac{30\left(-17\right)}{10}x-60<90-5-6x$$

Multiply 30 and -17 to get -510.

$$\frac{-510}{10}x-60<90-5-6x$$

Divide -510 by 10 to get -51.

$$-51x-60<90-5-6x$$

Subtract 5 from 90 to get 85.

$$-51x-60<85-6x$$

Add 6x to both sides.

$$-51x-60+6x<85$$

Combine -51x and 6x to get -45x.

$$-45x-60<85$$

Add 60 to both sides.

$$-45x<85+60$$

Add 85 and 60 to get 145.

$$-45x<145$$

Divide both sides by -45. Since -45 is negative, the inequality direction is changed.

$$x>\frac{145}{-45}$$

Reduce the fraction \frac{145}{-45} to lowest terms by extracting and canceling out 5.

$$x>-\frac{29}{9}$$