If 3|3 – x| = 7, what is the product of all the possible va

Question

If 3|3 – x| = 7, what is the product of all the possible values of x?

A. 1/9
B. 1/3
C. 2/3
D. 16/9
E. 32/9

Zarrolou · Accepted Answer

3|3 - x| = 7 
case  3-x>0 
 3(3-x)=7 
 9-3x=7, x=\frac{2}{3} 
case  3-x<0 
 3(-3+x)=7 
 -9+3x=7, x= 16/3

\frac{2}{3}*\frac{16}{3}=\frac{32}{9} 
E

WpackAlumDukeBound · Answer

3|3-x| = 7 can be rewritten as:  |3-x| = \frac{7}{3}

So

|\frac{9}{3} - x| = \frac{7}{3}

x has two possible solutions  \frac{2}{3}  and  \frac{16}{3}  that satisfy the equation

\frac{2}{3}*\frac{16}{3} = \frac{32}{9}

Answer is E

agrchandan · Answer

3|3 – x| = 7 So, |3 – x| = 7/3 or (3-x) = +7/3 or -7/3
Solving we get x = 2/3 or 16/3
product =  2/3 * 16/3 = 32/9

WholeLottaLove · Answer

If 3|3 – x| = 7, what is the product of all the possible values of x?

x≥3, x<3

x≥3: 
3|3 – x| = 7 
3 -(3-x) = 7
3 (-3+x) = 7
-9 + 3x = 7
3x = 16
x=16/3 Valid

x<3
3(3-x) = 7
9-3x = 7
-3x=-2
x=2/3

(16/3)*(2/3) = 32/9

(E)

Caesar_1987 · Answer

I don't agree with E. 16/3, when substituted in the original equation doesn't satisfy it. you would get |-9/3| = 7/3 which is not legit. So we should discard 16/3 as a solution of the equation. That leaves us with 2/3 which is option C

Best Regards
Dheeraj Rekula

Best Regards
Dheeraj Rekula

Bunuel · Answer

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Bunuel · Answer

16/3 does satisfy the equation: 
3|3 – 16/3| = 7;
3*7/3 = 7.

Hope it's clear.

eddy8700 · Answer

3|3-x| = 7 can be rewritten as: |3−x|=7/3
so we have 
1. 3-x =7/3
x=2/3

2. 3-x=-7/3
x=16/3

so product will be
 32/9

AkshdeepS · Answer

Given : 3|3 – x| = 7

3 – x = 7/3 or 3 – x = -7/3

x = 2/3 or 16/3

Product of all the possible values of x = 2/3 * 16*3 = 32/9

(E)

rickyreign · Answer

the equation leads to two values of x
2/3 , 16/3
their product equals to 32/9 i.e. E

Dwija01 · Answer

When |3-x| is -ve

9-3x=7
2=3x
x=2/3

when |3-x| is +ve
-9+3x=7
3x=16
x=16/3

2/3*16/3=32/9

If 3|3 – x| = 7, what is the product of all the possible va

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GMAT Problem Solving (PS) Questions

If 3|3 – x| = 7, what is the product of all the possible va

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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My Rewards