Solve x+4/4-3x-4/2<1/2

$$\frac { x + 4 } { 4 } - \frac { 3 x - 4 } { 2 } < \frac { 1 } { 2 }$$

Solve for x

$$x>2$$

Solution Steps

Multiply both sides of the equation by 4, the least common multiple of 4,2. Since 4 is positive, the inequality direction remains the same.

$$x+4-2\left(3x-4\right)<2$$

Use the distributive property to multiply -2 by 3x-4.

$$x+4-6x+8<2$$

Combine x and -6x to get -5x.

$$-5x+4+8<2$$

Add 4 and 8 to get 12.

$$-5x+12<2$$

Subtract 12 from both sides.

$$-5x<2-12$$

Subtract 12 from 2 to get -10.

$$-5x<-10$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$x>\frac{-10}{-5}$$

Divide -10 by -5 to get 2.

$$x>2$$