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If |x| < 20 and |x – 8| > |x + 4|, which of the following expresses the allowable range for x?
- a)–12 < x < 12
- b)–20 < x < 2
- c)–20 < x < –12 and 12 < x < 20
- d)–20 < x < –8 and 4 < x < 20
- e)–20 < x < –4 and 8 < x < 20
Correct answer is option 'B'. Can you explain this answer?
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If |x| < 20 and |x – 8| > |x + 4|, which of the following ...
To solve this inequality, we can break it down into two cases:
Case 1: x is positive or zero (x ≥ 0) If x is greater than or equal to 0, the inequality simplifies to: x - 8 > x + 4
By subtracting x from both sides, we get: -8 > 4
This inequality is false, so there are no solutions for x in this case.
Case 2: x is negative (x < 0) If x is less than 0, the inequality simplifies to: -(x - 8) > x + 4
Expanding the absolute values, we have: -1(x - 8) > x + 4
Simplifying further:
- x + 8 > x + 4
By subtracting x from both sides, we get: 8 > 2x + 4
Subtracting 4 from both sides: 4 > 2x
Dividing by 2: 2 > x
So, in this case, x must be less than 2.
Combining the results from both cases, we find that x must be less than 2. However, we also have the constraint that |x| < 20, which means x must be within the range -20 < x < 20.
Combining these conditions, the allowable range for x is -20 < x < 2, which corresponds to option (B).
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If |x| < 20 and |x – 8| > |x + 4|, which of the following ...
The absolute value of x, denoted |x|, represents the distance between x and 0 on the number line. It is always positive or zero.
For example, if x is 4, then |x| = |4| = 4, because 4 is 4 units away from 0 on the number line. Similarly, if x is -4, then |x| = |-4| = 4, because -4 is also 4 units away from 0 on the number line.
In general, |x| = x if x is positive or zero, and |x| = -x if x is negative.
For example, if x is 4, then |x| = |4| = 4, because 4 is 4 units away from 0 on the number line. Similarly, if x is -4, then |x| = |-4| = 4, because -4 is also 4 units away from 0 on the number line.
In general, |x| = x if x is positive or zero, and |x| = -x if x is negative.
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If |x| < 20 and |x – 8| > |x + 4|, which of the following expresses the allowable range for x?a)–12 < x < 12b)–20 < x < 2c)–20 < x < –12 and 12 < x < 20d)–20 < x < –8 and 4 < x < 20e)–20 < x < –4 and 8 < x < 20Correct answer is option 'B'. Can you explain this answer?
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If |x| < 20 and |x – 8| > |x + 4|, which of the following expresses the allowable range for x?a)–12 < x < 12b)–20 < x < 2c)–20 < x < –12 and 12 < x < 20d)–20 < x < –8 and 4 < x < 20e)–20 < x < –4 and 8 < x < 20Correct answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If |x| < 20 and |x – 8| > |x + 4|, which of the following expresses the allowable range for x?a)–12 < x < 12b)–20 < x < 2c)–20 < x < –12 and 12 < x < 20d)–20 < x < –8 and 4 < x < 20e)–20 < x < –4 and 8 < x < 20Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If |x| < 20 and |x – 8| > |x + 4|, which of the following expresses the allowable range for x?a)–12 < x < 12b)–20 < x < 2c)–20 < x < –12 and 12 < x < 20d)–20 < x < –8 and 4 < x < 20e)–20 < x < –4 and 8 < x < 20Correct answer is option 'B'. Can you explain this answer?.
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