SOLUTION: can someone help me solve this problem please Solve 3|x - 4| - 9 = 24 Smaller answer (nearest integer): Larger answer (nearest integer):

Algebra ->  Absolute-value -> SOLUTION: can someone help me solve this problem please Solve 3|x - 4| - 9 = 24 Smaller answer (nearest integer): Larger answer (nearest integer):       Log On


   

Question 772506: can someone help me solve this problem please
Solve 3|x - 4| - 9 = 24
Smaller answer (nearest integer):
Larger answer (nearest integer):
Found 2 solutions by josgarithmetic, Edwin McCravy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Treat the |x-4| as the variable and first solve for that. THEN examine the two conditions, x-4%3C0, and x-4%3E=0 and solve each of these conditions separately. Note, "conditions", are NOT the equations for you to solve; they are possibilities about x-4.




After further thinking knowing that this stuff is often complicated for people, here is more help, steps.

3%2Aabs%28x-4%29=24%2B9
3%2Aabs%28x-4%29=33
abs%28x-4%29=11 after dividing both sides by 3,
and now the conditions to check:

CONDITION:
x-4%3C0, abs%28x-4%29=4-x
abs%28x-4%29=11
4-x=11
-x=11-4
x=-7__________part of the answer

CONDITION:
x-4%3E=0, abs%28x-4%29=x-4
abs%28x-4%29=11
x-4=11
x=11%2B4
x=15________other part of answer

Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
This is the third time I have answered this exact same
problem with ONLY the numbers changed.  I merely copied
and pasted this one from the last one and changed the
numbers.  Nothing else was different.  I suspect that
you are the same person.  If you don't understand what's
going on, then tell me about it in the thank-you note.
If you're not studying and trying to learn what this is
all about, then I'm not doing anything but helping you
cheat.  Your teacher will find out you aren't doing
the homework but getting somebody to do it for you.  I'm
here to help you learn, not to help you cheat.  You won't
fool your teacher by cheating on homework.  Teachers
aren't fooled by perfect homework and terrible test 
grades.  I'll do just one more like this in case you're
somebody else, or really just can't get it.  If you can't
then tell me about it in the thank-you note. 

          
          3|x - 4| - 9 = 24
        
Add 9 from both sides

              3|x - 4| = 33

Divide both sides by 3

               |x - 4| = 11

That would be true whether x - 4 = 11 or whether it equals -11.
So we take both cases:

      x - 4 = 11           x - 4 = -11
          x = 15               x = -7

Smaller solution = -7, Larger solution = 15

Edwin