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

Algebra ->  Inequalities -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
#1

abs%285x%2B6%29%3E26 Start with the given inequality


Break up the absolute value (remember, if you have abs%28x%29%3E+a, then x+%3C+-a or x+%3E+a)

5x%2B6+%3C+-26 or 5x%2B6+%3E+26 Break up the absolute value inequality using the given rule




Now lets focus on the first inequality 5x%2B6+%3C+-26


5x%2B6%3C-26 Start with the given inequality


5x%3C-26-6Subtract 6 from both sides


5x%3C-32 Combine like terms on the right side


x%3C%28-32%29%2F%285%29 Divide both sides by 5 to isolate x



x%3C-32%2F5 Reduce


Now lets focus on the second inequality 5x%2B6+%3E+26


5x%2B6%3E26 Start with the given inequality


5x%3E26-6Subtract 6 from both sides


5x%3E20 Combine like terms on the right side


x%3E%2820%29%2F%285%29 Divide both sides by 5 to isolate x



x%3E4 Divide



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

Answer:

So our answer is

x+%3C+-32%2F5 or x+%3E+4


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



abs%282x-4%29=16 Start with the given equation


Break up the absolute value (remember, if you have abs%28x%29=a, then x=-a or x=a)

2x-4=-16 or 2x-4=16 Set the expression 2x-4 equal to the original value 16 and it's opposite -16




Now lets focus on the first equation 2x-4=-16


2x-4=-16 Start with the given equation


2x=-16%2B4Add 4 to both sides


2x=-12 Combine like terms on the right side


x=%28-12%29%2F%282%29 Divide both sides by 2 to isolate x



x=-6 Divide

--------------------------------------------------------------
Answer:
So our answer is x=-6




Now lets focus on the second equation 2x-4=16



2x-4=16 Start with the given equation


2x=16%2B4Add 4 to both sides


2x=20 Combine like terms on the right side


x=%2820%29%2F%282%29 Divide both sides by 2 to isolate x



x=10 Divide

--------------------------------------------------------------
Answer:
So our answer is x=10



So the solutions to abs%282x-4%29=16 are:

x=-6 and x=10



Notice if we graph y=abs%282x-4%29 and y=16 (just set each side equal to y and graph), we get


graph%28500%2C500%2C-20%2C20%2C-2%2C20%2Cabs%282x-4%29%2C16%29 Graph of y=abs%282x-4%29 (red) and y=16(green)

and we can see the two graphs intersect at x=-6 and x=10. So this verifies our answer.


Answer by edjones(8007) About Me  (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