Solve 7-1/2x>x+1

$$7 - \frac { 1 } { 2 } x > x + 1$$

Solve for x

$$x<4$$

Solution Steps

Subtract x from both sides.

$$7-\frac{1}{2}x-x>1$$

Combine -\frac{1}{2}x and -x to get -\frac{3}{2}x.

$$7-\frac{3}{2}x>1$$

Subtract 7 from both sides.

$$-\frac{3}{2}x>1-7$$

Subtract 7 from 1 to get -6.

$$-\frac{3}{2}x>-6$$

Multiply both sides by -\frac{2}{3}, the reciprocal of -\frac{3}{2}. Since -\frac{3}{2} is negative, the inequality direction is changed.

$$x<-6\left(-\frac{2}{3}\right)$$

Express -6\left(-\frac{2}{3}\right) as a single fraction.

$$x<\frac{-6\left(-2\right)}{3}$$

Multiply -6 and -2 to get 12.

$$x<\frac{12}{3}$$

Divide 12 by 3 to get 4.

$$x<4$$