Question

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

Answer 1

Answer is all real numbers.

<~~~~~~~~~~~~~~~~~~~~~~~~~~~~~>

---------(-3)---------------------(6)-------------

Explanation:

6b<36

Divide both sides by 6:

b<6

or

2b+12>6

Subtract 12 on both sides:

2b>-6

Divide both sides by 2:

b>-3

So we want to graph b<6 or b>-3:

o~~~~~~~~~~~~~~~~~~~~~~~~~~ b>-3

~~~~~~~~~~~~~~~~~~~~~~~~o b<6

_______(-3)____________(6)___________

So again "or" is a key word! Or means wherever you see shading for either inequality then that is a solution to the compound inequality. You see shading everywhere so the answer is all real numbers.

<~~~~~~~~~~~~~~~~~~~~~~~~~~~~~>

---------(-3)---------------------(6)-------------

Answer 2

All real numbers
`(-\infty, \infty)`

Explanation:

First we solve the following inequality

`6b < 36`

Divide by 6 both sides of the inequality

`b<(36)/(6)\\\\b<6`

The set of solutions is:

`(-\infty, 6)`

Now we solve the following inequality

`2b + 12 > 6`

Subtract 12 on both sides of the inequality

`2b + 12-12 > 6-12`

`2b> -6`

Divide by 2 on both sides of the inequality

`(2)/(2)b> -(6)/(2)`

`b> -3`

The set of solutions is:

`(-3, \infty)`

Finally, the set of solutions for composite inequality is:

`(-\infty, 6)` ∪
`(-3, \infty)`

This is: All real numbers
`(-\infty, \infty)`