Question

Solve |2g + 5| > 7. Show its equivalent compound sentence and its solution.

Answer 1

The first one would have no solution but what about the second one?

Answer 2

You know that absolute value expressions are never negative, but 2g + 5 can be either since we don't know the value of the variable. So we have to account for either possibility. this is what gives us the compound sentence referenced in the question. If 2g + 5 is negative then we can make it positive by negating it. If 2g + 5 is positive or zero them we don't have make any adjustment. Thus, the comp[ound sentence is:

-(2g + )| > 7 or 2g + 5 > 7

The "or" could be replaced with the union symbol.

I made a typo, this is corrected version.

Answer 3

Solution:

2g + 5 < -7 or 2g + 5 >7
2g < -12 or 2g > 12
g < -6 or g > 6

Answer 4

Ahh okay

Answer 5

got it?

Answer 6

Yes thanks

Answer 7

Except I made ANOTHER mistake! Look at the right side of the "or" in my solution. It should be:

2g + 5 > 7
2g > 2 (I had 12 here instead of 2)
g > 1

Answer 8

Here's the graphical solution (attached).