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

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

Solve for x

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

Solution Steps

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

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

Subtract 2 from 5 to get 3.

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

Subtract 3x from both sides.

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

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

$$-2x+3<2$$

Subtract 3 from both sides.

$$-2x<2-3$$

Subtract 3 from 2 to get -1.

$$-2x<-1$$

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

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

Fraction \frac{-1}{-2} can be simplified to \frac{1}{2} by removing the negative sign from both the numerator and the denominator.

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