Solve x+7/2-1<3x+2/2

$$\frac { x + 7 } { 2 } - 1 < \frac { 3 x + 2 } { 2 }$$

Solve for x

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

Solution Steps

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

$$x+7-2<3x+2$$

Subtract 2 from 7 to get 5.

$$x+5<3x+2$$

Subtract 3x from both sides.

$$x+5-3x<2$$

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

$$-2x+5<2$$

Subtract 5 from both sides.

$$-2x<2-5$$

Subtract 5 from 2 to get -3.

$$-2x<-3$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

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

Fraction \frac{-3}{-2} can be simplified to \frac{3}{2} by removing the negative sign from both the numerator and the denominator.

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