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|4x+24|= 96
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25 Dec 2018, 16:46
25 Dec 2018, 16:46
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65% (01:05) correct
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\(|4x+24|= 96\)
\(|4x|=120\)
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
_________________
\(|4x|=120\)
Quantity A |
Quantity B |
x |
18 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
_________________
Re: |4x+24|= 96
[#permalink]
27 Dec 2018, 09:07
27 Dec 2018, 09:07
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1
Bookmarks
Carcass wrote:
\(|4x+24|= 96\)
\(|4x|=120\)
\(|4x|=120\)
Quantity A |
Quantity B |
x |
18 |
There are 3 steps to solving equations involving ABSOLUTE VALUE:
1. Apply the rule that says: If |x| = k, then x = k and/or x = -k
2. Solve the resulting equations
3. Plug solutions into original equation to check for extraneous roots
GIVEN: |4x+24|= 96
So, EITHER 4x + 24 = 96 OR 4x + 24 = -96
If 4x + 24 = 96, then x = 18
If 4x + 24 = -96, then x = -30
Both x-values work upon testing
GIVEN: |4x|= 120
So, EITHER 4x = 120 OR 4x = -120
If 4x = 120, then x = 30
If 4x = -120, then x = -30
Both x-values work upon testing
IMPORTANT: Only ONE value (x = -30) satisfies BOTH equations, so x MUST equal -30
We get:
QUANTITY A: -30
QUANTITY B: 18
Answer: B
Cheers,
Brent
_________________
Re: |4x+24|= 96
[#permalink]
27 Dec 2018, 22:23
27 Dec 2018, 22:23
Expert Reply
Carcass wrote:
\(|4x+24|= 96\)
\(|4x|=120\)
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
\(|4x|=120\)
Quantity A |
Quantity B |
x |
18 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Hi..
Many ways..
(I) number line
Look at the problem from the number line view..
\(|4x+24|= 96\) means 4x is 96 units away from -24.
\(|4x|=120\) means 4x is 120 units away from 0.
Thus, 4x is closer to -24 than to 0. So 4x is negative and so is x.
A is negative and B is 18, so B>A.
(II) As both sides positive, square both sides.
\(|4x+24|= 96....|x+6|=24....x^2+12x+36=576....x^2+12x-540=0....(X+30)(x-18)=0\), so x is 18 or -30
\(|4x|=120.....|x|=30\), so x is 30 or -30..
Common is x is -30, so A is -30 and B is 18, so B>A.
(III) open the Modulus.
\(|4x+24|= 96\)
(a) 4x+24=96...4x=72...X=18
(b) 4x+24=-96...4x=-120...x=-30 AND
\(|4x|=120\)
(a) 4x=120...x=30
(b) 4x=-120...x=-30
Thus, x=-30 and B>A
B
More on modulus..
See the post in signature below
_________________
Some useful Theory.
1. Arithmetic and Geometric progressions : https://gre.myprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://gre.myprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://gre.myprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://gre.myprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://gre.myprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html
1. Arithmetic and Geometric progressions : https://gre.myprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://gre.myprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://gre.myprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://gre.myprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://gre.myprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html
Re: |4x+24|= 96
[#permalink]
04 Jan 2019, 17:40
04 Jan 2019, 17:40
Answer: B
|4x+24| = 96
|4x| = 120
From second expression:
We have |4x| = 120 so:
Either 4x=120 or -4x =120, So:
Either x =30 or x=-30
From first expression:
We have |4x+24| = 96
Either 4x+24 = 96 or -(4x+24) = 96
Considering both expression, we should look which one makes sense:
If x =30 then 4x+24 = 144
If x =-30 then 4x+24 = 96
So x should be -30 and is less than B
_________________
|4x+24| = 96
|4x| = 120
From second expression:
We have |4x| = 120 so:
Either 4x=120 or -4x =120, So:
Either x =30 or x=-30
From first expression:
We have |4x+24| = 96
Either 4x+24 = 96 or -(4x+24) = 96
Considering both expression, we should look which one makes sense:
If x =30 then 4x+24 = 144
If x =-30 then 4x+24 = 96
So x should be -30 and is less than B
_________________
Follow your heart
Re: |4x+24|= 96
[#permalink]
30 Jul 2023, 11:09
30 Jul 2023, 11:09
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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