Carcass wrote:
\(|4x+24|= 96\)
\(|4x|=120\)
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