Solve the compound inequality 6b < 36 or 2b + 12 > 6.

all values of b

Step-by-step explanation:

6b < 36 or 2b + 12 > 6.

First solve the one on the left

6b < 36

Divide by 6

6b/6 < 36/6

b  <6

Then solve the one on the right

2b + 12 > 6

Subtract 12 from each side

2b+12-12 >6-12

2b >-6

Divide by 2

2b/2 >-6/2

b >-3

b<6 or b >-3

Rewriting

b>-3  or b<6

b > -3 is an open circle at -3 with a line going to the right

b < 6 is an open circle at 6 with a line going to the left

The or means we add the lines together

We have a line going from negative infinity to infinity

all values of b

All real numbers  b ∈

Step-by-step explanation:

First we solve the following inequality

Divide by 6 both sides of the inequality

The set of solutions is:

Now we solve the following inequality

Subtract 12 on both sides of the inequality

Divide by 2 on both sides of the inequality

The set of solutions is:

Finally, the set of solutions for composite inequality is:

 ∪

This is: All real numbers