Question

Which value are in the solution set of the compound inequality?

Check all that apply.

4(x+3) ≤ 0 or 1/4x+1>3?

A.-6
B.-3
C.0
D.3
E.8
F.10

Answer 1

`4(x+3)\leq0\ \ \ \ |:4\\x+3\leq0\ \ \ |-3\\x\leq-3\\\\(1)/(4)x+1 \ \textgreater \ 3\ \ \ |-1\\(1)/(4)x \ \textgreater \ 2\ \ \ \ |\cdot4\\x \ \textgreater \ 8\\\\x\leq-3\ or\ x \ \textgreater \ 8\\\\Answer:\\A.\ -6\\B.\ -3\\F.\ 10`

Answer 2

Option A and B

Explanation:

We have 4(x+3) ≤ 0

x+3 ≤ 0

x ≤ -3

We also have
`(1)/(4x+1)>3`

`4x+1<(1)/(3)\\\\4x<(-2)/(3)\\\\x<(-1)/(6)`

We have x ≤ -3 and
`x<-(1)/(6)`

Only A and B satisfies both this conditions.