MA001 Unit 1 Test question 8


#1

The problem is:

-5|2+4X| = -32(X+3/4) - |X| +1

I cannot figure out how to do this problem. Is there a place where the problems are worked out so that we can see the process? Is there a section specifically for MA001? Right now I am so confused that I cannot even figure out the first step.


MA001 Unit 1 Test - Question 8
#2

This question is driving me crazy, too. I am glad I am not the only one. I thought absolute value equations were supposed to have two answers. To anyone who can help…the answer they are giving us is -11/17; I cannot figure out how to get it :person_frowning:


#3

It looks like the best step-by-step option is here:

It’s still a bit hard to follow; I agree that this is a difficult problem.


#4

Thank you!

The link to the page came up blank, but I was able to go to symbolab.com and enter the problem. The solution is difficult to follow and seems to involve procedures that I’m just starting to learn in MA001 Unit 2. At this point I cannot understand the solution presented at symbolab.com, but I’ll return to it after I’ve done more of Unit 2.

I’m grateful for the link to symbolab.com for use in future difficulties.


#5

I have not taken the Unit Test yet, but I am on the last segment. On Tyler Wallaces Beginning Algebra Lab Notebook Sum-Now of a woman and her daughter combined age of 38 if the woman is triple the daughter’s age in 9 years. I solved for 5 while the video Age Problems Sum Now solved for 33. I also couldn’t figure out the mosaic and engraving question on the homework or the wool and linen tapestries questions and I tried for hours! I am unsure how to tag but this conversation is alittle unrelated to the specific test question!


#6

I have an update: I solved the word problem I was having trouble with in homework by multiplying by the time difference. Took a week of muddling though. I thought about the actual problem at hand and I recall -1,0 from Intermediate Algebra some 25 years ago, but this doesn’t match the answer given, but I wanted to follow the series of responses. Still learning.


#7

I had problems with question 8 too. Unit1 didn’t show us the proper way for solving absolute value equations. You will find the correct answer by constructing piecewise definitions and evaluating the ranges. I will show this technique here.

-5|2+4X| = -32(X+3/4) - |X| +1

Step 1:
Take the expression that is inside the absolute value bars and set that expression equal to zero. Then solve for X. (This value for X is the critical value, because X changes sign at this value.)

For |2+4X| :
2 + 4X = 0
X = - 1/2

For |X| :
X = 0

Step 2:
Determine the sign of the expression inside the absolute value bars on both sides of the critical value. This is done by testing a value for X on each side of that critical value.

For 2 + 4X :
X = -1 --> 2 - 4 = -2 --> So |2 + 4X| is negative if X < -1/2
X = 1 --> 2 + 4 = 6 --> So |2 + 4X| is positive if X ≥ - 1/2 (The ≥ sign includes 0 as a positive number)

For X :
X = -1 --> So |X| is negative if X < 0
X = 1 --> So |X| is positive if X ≥ 0 (Again, the ≥ sign includes 0 as a positive number)

Step 3:
Construct piecewise definitions.

|2 + 4X|=
-(2 + 4X) if X < - 1/2 {A}
(2 + 4X) if X ≥ - 1/2 {B}

|X| =
-(X) if X < 0 {C}
(X) if X ≥ 0 {D}

Step 4:
Determine the ranges and evaluate the expression for the ranges.

There are 3 ranges:
X < - 1/2

  • 1/2 ≤ X < 0
    X ≥ 0

Evaluate for X < - 1/2 (use {A} and {C}) : -5 (-2-4X) = -32 (X + 3/4) - (-X) + 1

This will result in X = - 11/17
-11/17 < -1/2, so the solution is correct!

Evaluate for -1/2 ≤ X < 0 (use {B} and {C}) : -5 (2+4X) = -32 (X + 3/4) - (-X) + 1

This will result in X = - 13/11

  • 13/11 < - 1/2, so the solution is false!

Evaluate for X > 0 (use {B} and {D}) : -5 (2+4X) = -32 (X + 3/4) - X + 1

This will result in X = -1
-1 < 0, so the solution is false!

The correct answer is - 11/17 !!!


MA001 Unit 1 Test - Question 8
#8

Thank you so very much!