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
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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
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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
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