Solve 3-8-a/2+8-a/6<0

$$3- \frac{ 8-a }{ 2 } + \frac{ 8-a }{ 6 } < 0$$

Solve for a

$$a<-1$$

Solution Steps

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

$$18-3\left(8-a\right)+8-a<0$$

Use the distributive property to multiply -3 by 8-a.

$$18-24+3a+8-a<0$$

Subtract 24 from 18 to get -6.

$$-6+3a+8-a<0$$

Add -6 and 8 to get 2.

$$2+3a-a<0$$

Combine 3a and -a to get 2a.

$$2+2a<0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$2a<-2$$

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

$$a<\frac{-2}{2}$$

Divide -2 by 2 to get -1.

$$a<-1$$