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

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

Solve for a

$$a>2$$

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.

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

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

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

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

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

Add 4 and 8 to get 12.

$$-5a+12<2$$

Subtract 12 from both sides.

$$-5a<2-12$$

Subtract 12 from 2 to get -10.

$$-5a<-10$$

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

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

Divide -10 by -5 to get 2.

$$a>2$$