Solve -x-2/4<3x+1/5+2

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

Solve for x

$$x>-2$$

Solution Steps

Multiply both sides of the equation by 20, the least common multiple of 4,5. Since 20 is positive, the inequality direction remains the same.

$$-5\left(x-2\right)<4\left(3x+1\right)+40$$

Use the distributive property to multiply -5 by x-2.

$$-5x+10<4\left(3x+1\right)+40$$

Use the distributive property to multiply 4 by 3x+1.

$$-5x+10<12x+4+40$$

Add 4 and 40 to get 44.

$$-5x+10<12x+44$$

Subtract 12x from both sides.

$$-5x+10-12x<44$$

Combine -5x and -12x to get -17x.

$$-17x+10<44$$

Subtract 10 from both sides.

$$-17x<44-10$$

Subtract 10 from 44 to get 34.

$$-17x<34$$

Divide both sides by -17. Since -17 is negative, the inequality direction is changed.

$$x>\frac{34}{-17}$$

Divide 34 by -17 to get -2.

$$x>-2$$