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

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

Solve for x

$$x>2$$

Solution Steps

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

$$2x+6<4x-2+x+2$$

Combine 4x and x to get 5x.

$$2x+6<5x-2+2$$

Add -2 and 2 to get 0.

$$2x+6<5x$$

Subtract 5x from both sides.

$$2x+6-5x<0$$

Combine 2x and -5x to get -3x.

$$-3x+6<0$$

Subtract 6 from both sides. Anything subtracted from zero gives its negation.

$$-3x<-6$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

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

Divide -6 by -3 to get 2.

$$x>2$$