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

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

Solve for x

$$x>-33$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.

$$2x-3\left(x+1\right)<30$$

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

$$2x-3x-3<30$$

Combine 2x and -3x to get -x.

$$-x-3<30$$

Add 3 to both sides.

$$-x<30+3$$

Add 30 and 3 to get 33.

$$-x<33$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x>-33$$