Given |2x + 5| = 9, find the solutions

Question

I need help finding the answer please.

Answer 1

Hi Cherokee--

 

So the object here is to make whatever is in between the "absolute value" signs equal either 9 or -9.

 

Why? Because absolute value basically means "distance away from something." So whether it's positive or negative to begin with, it's still going to be 9 steps away from zero on a number line.

 

So: let's deal with positive first. 2x + 5 = 9, so 2x = 4, so x = 2

 

One of your solutions is 2.

 

Now, what number for x will make everything inside the brackets equal negative 9?

 

2x + 5 = -9, so 2x = -14, so x = -7

 

Again, it works because the absolute value of -9 is 9 (think 9 steps on a number line--either direction you go, it's still 9 steps!)

 

So your 2 solutions are 2 and -7

 

Hope this helps!

 

Matt in NY