SOLUTION: I am having problems absolute value solving inequalities. I have two problems. I think I solved them, but I am not 100% sure. |5x+6|>26 x| x<-4 or x>4 the second problem is

Question 107469: I am having problems absolute value solving inequalities. I have two problems. I think I solved them, but I am not 100% sure.
|5x+6|>26
x| x<-4 or x>4
the second problem is:
|2x-4| =16
x= -6 and 10
Found 2 solutions by jim_thompson5910, edjones:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
#1

Start with the given inequality

Break up the absolute value (remember, if you have , then or )

or Break up the absolute value inequality using the given rule

Now lets focus on the first inequality

Start with the given inequality

Subtract 6 from both sides

Combine like terms on the right side

Divide both sides by 5 to isolate x

Reduce

Now lets focus on the second inequality

Start with the given inequality

Subtract 6 from both sides

Combine like terms on the right side

Divide both sides by 5 to isolate x

Divide

----------------------------------------------------

Answer:

So our answer is

or

which looks like this in interval notation

if you wanted to graph the solution set, you would get

Graph of the solution set in blue and the excluded values represented by open circles

#2

Start with the given equation

Break up the absolute value (remember, if you have , then or )

or Set the expression equal to the original value 16 and it's opposite -16

Now lets focus on the first equation

Start with the given equation

Add 4 to both sides

Combine like terms on the right side

Divide both sides by 2 to isolate x

Divide

--------------------------------------------------------------
Answer:
So our answer is

Now lets focus on the second equation

Start with the given equation

Add 4 to both sides

Combine like terms on the right side

Divide both sides by 2 to isolate x

Divide

--------------------------------------------------------------
Answer:
So our answer is

So the solutions to are:

and

Notice if we graph and (just set each side equal to y and graph), we get

Graph of (red) and (green)

and we can see the two graphs intersect at and . So this verifies our answer.

Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
|5x+6|>26
.
5x+6>26
5x>20
x>4
.
5x+6<-26
5x<-32
x<-32/5
.
The second problem is correct.
.
Ed