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

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If 3|3 – x| = 7, what is the product of all the possible va [#permalink]  28 Mar 2013, 20:09
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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
[Reveal] Spoiler: OA
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Kudos [?]: 24 [2] , given: 18

Re: If 3|3 – x| = 7, what is the product of all the possible va [#permalink]  28 Mar 2013, 20:40
2
KUDOS
nave81 wrote:
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

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

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

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Kudos [?]: 1530 [1] , given: 219

Re: If 3|3 – x| = 7, what is the product of all the possible va [#permalink]  28 Mar 2013, 23:29
1
KUDOS
$$3|3 - x| = 7$$
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
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Kudos [?]: 22 [0], given: 6

Re: If 3|3 – x| = 7, what is the product of all the possible va [#permalink]  01 Apr 2013, 07:00
nave81 wrote:
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

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 = $$2/3 * 16/3 = 32/9$$
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Kudos [?]: 99 [0], given: 134

Re: If 3|3 – x| = 7, what is the product of all the possible va [#permalink]  10 Jul 2013, 09:38
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)
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Re: If 3|3 – x| = 7, what is the product of all the possible va [#permalink]  23 Jan 2015, 00:33
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Re: If 3|3 – x| = 7, what is the product of all the possible va   [#permalink] 23 Jan 2015, 00:33
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