Answer :
Answer:
TL;DR
g < -3
g > 11/2
There are two solutions to your inequality.
Step-by-step explanation:
First, we need to clear the absolute value bars to find the solution to this inequality by creating two cases of this inequality. The positive case, and the negative case.
The Negative Case
-(4g -5)
The Positive Case
(4g -5)
Let’s use the negative case first.
-(4g -5) is like multiplying -1(4g -5). So you get -4g + 5
Next let’s compare it to 17: -4g + 5 > 17
Now, subtract five from both sides
-4g > 12
Now divide by -4 to isolate g.
-g > 3
g < -3
Remember, when we solve for g, we always switch the symbol.
Now, for the positive case:
4g - 5 > 17
Let’s add 5 to both sides.
4g > 22
Let’s now divide by 4.
g > 11/2 or 5.5.
So, there are two solutions for this inequality.
g > 11/2
g < -3
In interval notation we can write it like this:
(-∞,-3) - From Negative Infinity to Negative 3
(11/2,+∞) - From Positive 11/2 to Positive Infinity
