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Og Inequality Q

This topic has 5 expert replies and 0 member replies
AbeNeedsAnswers Master | Next Rank: 500 Posts Default Avatar
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Og Inequality Q

Post Wed Jul 19, 2017 10:00 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Which of the following is equivalent to the pair of inequalities x + 6 > 10 and x - 3 <= 5 ?

    (A) 2 <= x < 16
    (B) 2 <= x < 4
    (C) 2 < x <= 8
    (D) 4 < x <= 8
    (E) 4 <= x < 16

    D

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    Post Wed Jul 19, 2017 10:22 pm
    AbeNeedsAnswers wrote:
    Which of the following is equivalent to the pair of inequalities x + 6 > 10 and x - 3 <= 5 ?

    (A) 2 <= x < 16
    (B) 2 <= x < 4
    (C) 2 < x <= 8
    (D) 4 < x <= 8
    (E) 4 <= x < 16

    D
    We have two inequalities: x + 6 > 10 and x - 3 ≤ 5;

    1. x + 6 > 10 => x > 4
    2. x - 3 ≤ 5 => x ≤ 8

    Together, we get

    4 < x ≤ 8

    We see that Option D is correct.

    The correct answer: D

    Hope this helps!

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    Post Thu Jul 20, 2017 12:02 pm
    Hi AbeNeedsAnswers,

    When dealing with multiple inequalities, it can be helpful to simplify the inequalities one-at-a-time and use the results to help you 'narrow down' the possibilities.

    Here, the first inequality is X + 6 > 10. Simplifying that, we get...

    X + 6 > 10
    X > 4

    Looking at the answer choices, there's only ONE answer that includes X > 4.... Just to be sure though, let's see what happens with the second inequality....

    X - 3 <= 5
    X <= 8

    That confirms the correct answer.

    Final Answer: D

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    Post Sun Jul 23, 2017 3:24 pm
    I'd simplify the inequalities then graft them together.

    The first one: x + 6 > 10 => x > 4

    The second one: 5 ≥ x - 3 => 8 ≥ x

    Since x is the middle term, we use it to connect them: 8 ≥ x > 4.

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    Post Mon Jul 24, 2017 11:52 am
    AbeNeedsAnswers wrote:
    Which of the following is equivalent to the pair of inequalities x + 6 > 10 and x - 3 <= 5 ?

    (A) 2 ≤ x < 16
    (B) 2 ≤ x < 4
    (C) 2 < x ≤ 8
    (D) 4 < x ≤ 8
    (E) 4 ≤ x < 16
    Another approach is to eliminate 4 of the answer choices

    First, x + 6 > 10 can be rewritten as x > 4
    This means that x CANNOT equal 3
    When we check the answer choices, we see that A, B and C all say that x COULD equal 3
    So, eliminate A, B and C

    Second, x - 3 ≤ 5 can be rewritten as x ≤ 8
    This means that x CANNOT equal 9
    When we check the remaining answer choices, we see that E says that x COULD equal 9
    So, eliminate E

    We're left with D


    Cheers,
    Brent

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    Post Tue Jul 25, 2017 11:00 am
    AbeNeedsAnswers wrote:
    Which of the following is equivalent to the pair of inequalities x + 6 > 10 and x - 3 <= 5 ?

    (A) 2 <= x < 16
    (B) 2 <= x < 4
    (C) 2 < x <= 8
    (D) 4 < x <= 8
    (E) 4 <= x < 16
    We are given two inequalities:

    x + 6 > 10

    x > 4, which is equivalent to 4 < x

    and

    x - 3 ≤ 5

    x ≤ 8

    So we have:

    4 < x ≤ 8

    Answer: D

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