Solve x+1/5-2x-1/2>3

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

Solve for x

$$x<-\frac{23}{8}$$

Solution Steps

Multiply both sides of the equation by 10, the least common multiple of 5,2. Since 10 is positive, the inequality direction remains the same.

$$2\left(x+1\right)-5\left(2x-1\right)>30$$

Use the distributive property to multiply 2 by x+1.

$$2x+2-5\left(2x-1\right)>30$$

Use the distributive property to multiply -5 by 2x-1.

$$2x+2-10x+5>30$$

Combine 2x and -10x to get -8x.

$$-8x+2+5>30$$

Add 2 and 5 to get 7.

$$-8x+7>30$$

Subtract 7 from both sides.

$$-8x>30-7$$

Subtract 7 from 30 to get 23.

$$-8x>23$$

Divide both sides by -8. Since -8 is negative, the inequality direction is changed.

$$x<-\frac{23}{8}$$