Solve 3(x+2)-4x<x-3

$$3 ( x + 2 ) - 4 x < x - 3$$

Solve for x

$$x>\frac{9}{2}$$

Solution Steps

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

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

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

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

Subtract x from both sides.

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

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

$$-2x+6<-3$$

Subtract 6 from both sides.

$$-2x<-3-6$$

Subtract 6 from -3 to get -9.

$$-2x<-9$$

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

$$x>\frac{-9}{-2}$$

Fraction \frac{-9}{-2} can be simplified to \frac{9}{2} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{9}{2}$$