Solve x+3/8-x+3/7<3/14

$$\frac { x + 3 } { 8 } - \frac { x + 3 } { 7 } < \frac { 3 } { 14 }$$

Solve for x

$$x>-15$$

Solution Steps

Multiply both sides of the equation by 56, the least common multiple of 8,7,14. Since 56 is positive, the inequality direction remains the same.

$$7\left(x+3\right)-8\left(x+3\right)<12$$

Use the distributive property to multiply 7 by x+3.

$$7x+21-8\left(x+3\right)<12$$

Use the distributive property to multiply -8 by x+3.

$$7x+21-8x-24<12$$

Combine 7x and -8x to get -x.

$$-x+21-24<12$$

Subtract 24 from 21 to get -3.

$$-x-3<12$$

Add 3 to both sides.

$$-x<12+3$$

Add 12 and 3 to get 15.

$$-x<15$$

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

$$x>-15$$