Solve x/2-7/8<7/8+x

$$\frac { x } { 2 } - \frac { 7 } { 8 } < \frac { 7 } { 8 } + x$$

Solve for x

$$x>-\frac{7}{2}$$

Solution Steps

Multiply both sides of the equation by 8, the least common multiple of 2,8. Since 8 is positive, the inequality direction remains the same.

$$4x-7<7+8x$$

Subtract 8x from both sides.

$$4x-7-8x<7$$

Combine 4x and -8x to get -4x.

$$-4x-7<7$$

Add 7 to both sides.

$$-4x<7+7$$

Add 7 and 7 to get 14.

$$-4x<14$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

$$x>\frac{14}{-4}$$

Reduce the fraction \frac{14}{-4} to lowest terms by extracting and canceling out 2.

$$x>-\frac{7}{2}$$