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# If 3x^2 + 2x + 9 = 2x^2 + 9x + 3, what all the possible values of x ?

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Intern
Joined: 30 Aug 2017
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If 3x^2 + 2x + 9 = 2x^2 + 9x + 3, what all the possible values of x ?  [#permalink]

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25 Sep 2017, 05:11
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73% (00:56) correct 27% (00:51) wrong based on 55 sessions

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If 3x^2 + 2x + 9 = 2x^2 + 9x + 3, what all the possible values of x ?

A. -6 and -1
B. -6 and 1
C. -1 and 6
D. 1 and 6
E. it cannot be determined from the information given.

Could someone expand on this pls?
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If 3x^2 + 2x + 9 = 2x^2 + 9x + 3, what all the possible values of x ?  [#permalink]

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25 Sep 2017, 07:50
nmargot wrote:
If 3x^2 + 2x + 9 = 2x^2 + 9x + 3, what all the possible values of x ?

A. -6 and -1
B. -6 and 1
C. -1 and 6
D. 1 and 6
E. it cannot be determined from the information given.

Could someone expand on this pls?

I will try, but I'm not sure exactly where you are confused.

$$3x^2 + 2x + 9 = 2x^2 + 9x + 3$$ gives you an equation from which to work. Get everything on one side, with 0 on the other. You are trying to "solve for x," to find out what x equals.

$$(3x^2 - 2x^2) + (2x - 9x) + (9 - 3) = 0$$

$$x^2 - 7x + 6 = 0$$ is just a quadratic equation. Find the roots, the solutions, that satisfy the quadratic equation.

"What [are] all the possible values of x" means "find the roots," which requires that you factor the quadratic.

$$x^2 - 7x + 6 = 0$$
$$(x - 6)(x - 1) = 0$$

By the zero product rule (if a*b = 0, then a = 0 or b = 0, out both a and b = 0), where the two expressions in parentheses are equivalent to the "a" and "b" in the rule:

$$x - 6 = 0, x = 6$$ OR
$$x - 1 = 0, x = 1$$
or both

When you plug x = 1 and x = 6 into the original two quadratics, both numbers work. For (x = 1) 14 = 14, and for (x = 6), 129 = 129.

There can be zero, one, or two solutions to a quadratic equation, depending on what is called the "discriminant."

This time there are two roots, two possible values of x.

They are 1 and 6.

Does that help?
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Re: If 3x^2 + 2x + 9 = 2x^2 + 9x + 3, what all the possible values of x ?  [#permalink]

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25 Sep 2017, 08:05
nmargot wrote:
If 3x^2 + 2x + 9 = 2x^2 + 9x + 3, what all the possible values of x ?

A. -6 and -1
B. -6 and 1
C. -1 and 6
D. 1 and 6
E. it cannot be determined from the information given.

Could someone expand on this pls?

7. Algebra

For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
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Re: If 3x^2 + 2x + 9 = 2x^2 + 9x + 3, what all the possible values of x ?  [#permalink]

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25 Sep 2017, 08:30
nmargot wrote:
If $$3x^2 + 2x + 9 = 2x^2 + 9x + 3$$, what all the possible values of x ?

A. -6 and -1
B. -6 and 1
C. -1 and 6
D. 1 and 6
E. it cannot be determined from the information given.

Could someone expand on this pls?

$$3x^2 + 2x + 9 = 2x^2 + 9x + 3$$

Or, $$x^2 - 7x + 6 = 0$$

Or, $$x^2 -x -6x + 6 = 0$$

Or, $$x(x - 1) -6 (x - 1) = 0$$

So, $$x = 1$$ & $$6$$, thus answer must be (D)

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Re: If 3x^2 + 2x + 9 = 2x^2 + 9x + 3, what all the possible values of x ?  [#permalink]

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25 Sep 2017, 09:36
nmargot wrote:
If 3x^2 + 2x + 9 = 2x^2 + 9x + 3, what all the possible values of x ?

A. -6 and -1
B. -6 and 1
C. -1 and 6
D. 1 and 6
E. it cannot be determined from the information given.

Could someone expand on this pls?

$$3x^2 + 2x + 9 = 2x^2 + 9x + 3$$
=> $$x^2 - 7x + 6 = 0$$
=> $$x^2 - 6x - x + 6 = 0$$
=> $$x(x- 6) - (x - 6) = 0$$
=> $$(x- 6) (x + 1) = 0$$

So as ab =0 => either a =0 or b=0 or both a and b are = 0

So here we can say x-6 =0 or x-1 =0
=> x= 6 or x=1
=> x can take either value and it will satisfy the given equation.

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Re: If 3x^2 + 2x + 9 = 2x^2 + 9x + 3, what all the possible values of x ?  [#permalink]

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26 Sep 2017, 16:26
nmargot wrote:
If 3x^2 + 2x + 9 = 2x^2 + 9x + 3, what all the possible values of x ?

A. -6 and -1
B. -6 and 1
C. -1 and 6
D. 1 and 6
E. it cannot be determined from the information given.

Let’s simplify the given equation:

3x^2 + 2x + 9 = 2x^2 + 9x + 3

x^2 - 7x + 6 = 0

(x - 6)(x - 1) = 0

x = 6 or x = 1

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Re: If 3x^2 + 2x + 9 = 2x^2 + 9x + 3, what all the possible values of x ? &nbs [#permalink] 26 Sep 2017, 16:26
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