Question

How do you solve `3 abs(5g+2) -8 ≥ 7` and find any extraneous solutions?

Answer 1

This inequality will hold true if the `g` values are greater than or equal to `3/5`, or less than or equal to `-7/5` The solution is not extraneous.

Explanation:

First, we isolate `abs(5g+2)`
`3abs(5g+2)-8>=7`
`3abs(5g+2)>=15`
`abs(5g+2)>=5`

Since the variable side is larger than the number side, we know this is a disjunction. Therefore, we write down the two possibilities.
`5g+2>=5`
`5g+2<=-5`

Solve each one.
`5g+2>=5`
`5g>=3`
`g>=3/5`

`5g+2<=-5`
`5g<=-7`
`g<=-7/5`

This means that this inequality will hold true if the `g` values are greater than or equal to `3/5` ,or less than or equal to `-7/5` These values are not extraneous, since they use "or" between the two different situations instead of "and". If this somehow were a conjunction, this would have been extraneous.