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If 4x-12 >= x + 9, which of the following must be true?

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by BTGmoderatorLU » Tue Feb 13, 2018 1:21 pm
$$If\ 4x-12\ge x+9,$$ Which of the following must be true?

A. x > 6
B. x < 7
C. x > 7
D. x > 8
E. x < 8

The OA is A.

Experts, to solve this PS question, can I isolate the x and get the answer, right?

$$3x\ge21$$
$$x\ge7$$
But why only A is true? What about C and D? Experts, any suggestion? Thanks in advance.
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If 4x-12 >= x + 9, which of the following must be true?

by EconomistGMATTutor » Tue Feb 13, 2018 1:41 pm
$$If\ 4x-12\ge x+9,$$ Which of the following must be true?

A. x > 6
B. x < 7
C. x > 7
D. x > 8
E. x < 8

The OA is A.

Experts, to solve this PS question, can I isolate the x and get the answer, right?

$$3x\ge21$$
$$x\ge7$$
But why only A is true? What about C and D? Experts, any suggestion? Thanks in advance.
Hi LUANDATO,
Let's take a look at your question.

$$4x-12\ge x+9$$
$$4x-12+12\ge x+9+12$$
$$4x\ge x+21$$
$$4x-x\ge x+21-x$$
$$3x\ge21$$
$$\frac{3x}{3}\ge\frac{21}{3}$$
$$x\ge7$$

The answer is x is greater than or equal to 7.
We can see that option B, C, D and E does not include x = 7.
Option A is x>6, which means in this interval x = 7 is included as well as values greater than 7.

Therefore, Option A is correct.

Does that make sense?
I am available if you'd like any follow up.
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by [email protected] » Tue Feb 13, 2018 5:05 pm
Hi LUANDATO,

You've correctly defined the range of values that X could be (re: X could equal 7 or anything greater than 7). You have to remember to answer the question that is ASKED though; we're asked what MUST be true. Only one answer will contain all of the solutions that you are looking for (the other 4 answers ignore some or all of the solutions). No matter what value of X you choose from the given range, it will ALWAYS be greater than 6.

Final Answer: A

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by Scott@TargetTestPrep » Thu Feb 15, 2018 10:36 am
LUANDATO wrote:$$If\ 4x-12\ge x+9,$$ Which of the following must be true?

A. x > 6
B. x < 7
C. x > 7
D. x > 8
E. x < 8
Simplifying the inequality we have:

4x - 12 ≥ x + 9

3x ≥ 21

x ≥ 7

If x is greater than or equal to 7, then it must be greater than 6. For example, if x = 7, we see that only answer choice A captures x = 7. No matter what value of x is chosen (as long as x ≥ 7), we are guaranteed that the value of x that has been chosen will indeed be greater than 6.

Answer: A

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