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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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\(|4x+24|= 96\)
\(|4x|=120\)
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.
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Re: |4x+24|= 96
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27 Dec 2018, 09:07
27 Dec 2018, 09:07
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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
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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
