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

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

Solve for x

$$x>6$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 2,3. Since 6 is positive, the inequality direction remains the same.

$$3\left(x+2\right)-2\left(2x-3\right)<6$$

Use the distributive property to multiply 3 by x+2.

$$3x+6-2\left(2x-3\right)<6$$

Use the distributive property to multiply -2 by 2x-3.

$$3x+6-4x+6<6$$

Combine 3x and -4x to get -x.

$$-x+6+6<6$$

Add 6 and 6 to get 12.

$$-x+12<6$$

Subtract 12 from both sides.

$$-x<6-12$$

Subtract 12 from 6 to get -6.

$$-x<-6$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x>\frac{-6}{-1}$$

Fraction \frac{-6}{-1} can be simplified to 6 by removing the negative sign from both the numerator and the denominator.

$$x>6$$