GMAT Exam > GMAT Questions > If x is a positive number and |-4x + 8| Ͱ...
Start Learning for Free
If x is a positive number and |-4x + 8| ≥ 2, which of the following statements is correct?
- a)No value of x satisfies this inequality
- b)0 < x ≤ 3/2 or x ≥ 5/2
- c)3/2 ≤ x ≤ 5/2
- d)|x| > 1
- e)x|x| < 4
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If x is a positive number and |-4x + 8| ≥ 2, which of the follow...
We know that |-4x + 8| = |-(4x -8)| = |4x -8|
Therefore we’re essentially given
|4x−8|≥2
Dividing both sides by 4, we get:
Representing this on the number line: 
Therefore we have
x ≥ 2.5 or x ≤ 1.5
Correct Answer: B
Most Upvoted Answer
If x is a positive number and |-4x + 8| ≥ 2, which of the follow...
**Given information:**
- x is a positive number
- |-4x + 8| ≤ 2
**To find:**
Which of the following statements is correct?
**Solution:**
Let's analyze each option one by one.
**Option a) No value of x satisfies this inequality:**
- This statement is not correct because there are values of x that satisfy the inequality.
**Option b) 0 ≤ x ≤ 3/2 or x ≥ 5/2:**
- To determine if this statement is correct, let's solve the inequality.
- |-4x + 8| ≤ 2
- We can rewrite the inequality as two separate inequalities:
- -4x + 8 ≤ 2 and -(-4x + 8) ≤ 2
- Simplifying both inequalities, we get:
- -4x ≤ -6 and 4x ≤ 10
- Dividing both sides of each inequality by -4, we get:
- x ≥ 3/2 and x ≤ 5/2
- Combining the two inequalities, we have:
- 3/2 ≤ x ≤ 5/2
- Therefore, the statement is correct.
**Option c) 3/2 ≤ x ≤ 5/2:**
- This statement is incorrect because it is missing the case where x can be equal to 0.
**Option d) |x| ≤ 1:**
- This statement is incorrect because it assumes that x can only be between -1 and 1, but x is defined as a positive number.
**Option e) x|x| ≤ 4:**
- This statement is incorrect because it assumes that x can only be between -2 and 2, but x is defined as a positive number.
Therefore, the correct answer is option **b) 0 ≤ x ≤ 3/2 or x ≥ 5/2**.
- x is a positive number
- |-4x + 8| ≤ 2
**To find:**
Which of the following statements is correct?
**Solution:**
Let's analyze each option one by one.
**Option a) No value of x satisfies this inequality:**
- This statement is not correct because there are values of x that satisfy the inequality.
**Option b) 0 ≤ x ≤ 3/2 or x ≥ 5/2:**
- To determine if this statement is correct, let's solve the inequality.
- |-4x + 8| ≤ 2
- We can rewrite the inequality as two separate inequalities:
- -4x + 8 ≤ 2 and -(-4x + 8) ≤ 2
- Simplifying both inequalities, we get:
- -4x ≤ -6 and 4x ≤ 10
- Dividing both sides of each inequality by -4, we get:
- x ≥ 3/2 and x ≤ 5/2
- Combining the two inequalities, we have:
- 3/2 ≤ x ≤ 5/2
- Therefore, the statement is correct.
**Option c) 3/2 ≤ x ≤ 5/2:**
- This statement is incorrect because it is missing the case where x can be equal to 0.
**Option d) |x| ≤ 1:**
- This statement is incorrect because it assumes that x can only be between -1 and 1, but x is defined as a positive number.
**Option e) x|x| ≤ 4:**
- This statement is incorrect because it assumes that x can only be between -2 and 2, but x is defined as a positive number.
Therefore, the correct answer is option **b) 0 ≤ x ≤ 3/2 or x ≥ 5/2**.
|
Explore Courses for GMAT exam
|
|
Similar GMAT Doubts
Top Courses for GMATView all
If x is a positive number and |-4x + 8| ≥ 2, which of the following statements is correct?a)No value of x satisfies this inequalityb)0 < x ≤ 3/2 or x ≥ 5/2c)3/2 ≤ x ≤ 5/2d)|x| > 1e)x|x| < 4Correct answer is option 'B'. Can you explain this answer?
Question Description
If x is a positive number and |-4x + 8| ≥ 2, which of the following statements is correct?a)No value of x satisfies this inequalityb)0 < x ≤ 3/2 or x ≥ 5/2c)3/2 ≤ x ≤ 5/2d)|x| > 1e)x|x| < 4Correct 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 is a positive number and |-4x + 8| ≥ 2, which of the following statements is correct?a)No value of x satisfies this inequalityb)0 < x ≤ 3/2 or x ≥ 5/2c)3/2 ≤ x ≤ 5/2d)|x| > 1e)x|x| < 4Correct 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 is a positive number and |-4x + 8| ≥ 2, which of the following statements is correct?a)No value of x satisfies this inequalityb)0 < x ≤ 3/2 or x ≥ 5/2c)3/2 ≤ x ≤ 5/2d)|x| > 1e)x|x| < 4Correct answer is option 'B'. Can you explain this answer?.
If x is a positive number and |-4x + 8| ≥ 2, which of the following statements is correct?a)No value of x satisfies this inequalityb)0 < x ≤ 3/2 or x ≥ 5/2c)3/2 ≤ x ≤ 5/2d)|x| > 1e)x|x| < 4Correct 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 is a positive number and |-4x + 8| ≥ 2, which of the following statements is correct?a)No value of x satisfies this inequalityb)0 < x ≤ 3/2 or x ≥ 5/2c)3/2 ≤ x ≤ 5/2d)|x| > 1e)x|x| < 4Correct 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 is a positive number and |-4x + 8| ≥ 2, which of the following statements is correct?a)No value of x satisfies this inequalityb)0 < x ≤ 3/2 or x ≥ 5/2c)3/2 ≤ x ≤ 5/2d)|x| > 1e)x|x| < 4Correct answer is option 'B'. Can you explain this answer?.
Solutions for If x is a positive number and |-4x + 8| ≥ 2, which of the following statements is correct?a)No value of x satisfies this inequalityb)0 < x ≤ 3/2 or x ≥ 5/2c)3/2 ≤ x ≤ 5/2d)|x| > 1e)x|x| < 4Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.
Here you can find the meaning of If x is a positive number and |-4x + 8| ≥ 2, which of the following statements is correct?a)No value of x satisfies this inequalityb)0 < x ≤ 3/2 or x ≥ 5/2c)3/2 ≤ x ≤ 5/2d)|x| > 1e)x|x| < 4Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If x is a positive number and |-4x + 8| ≥ 2, which of the following statements is correct?a)No value of x satisfies this inequalityb)0 < x ≤ 3/2 or x ≥ 5/2c)3/2 ≤ x ≤ 5/2d)|x| > 1e)x|x| < 4Correct answer is option 'B'. Can you explain this answer?, a detailed solution for If x is a positive number and |-4x + 8| ≥ 2, which of the following statements is correct?a)No value of x satisfies this inequalityb)0 < x ≤ 3/2 or x ≥ 5/2c)3/2 ≤ x ≤ 5/2d)|x| > 1e)x|x| < 4Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of If x is a positive number and |-4x + 8| ≥ 2, which of the following statements is correct?a)No value of x satisfies this inequalityb)0 < x ≤ 3/2 or x ≥ 5/2c)3/2 ≤ x ≤ 5/2d)|x| > 1e)x|x| < 4Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If x is a positive number and |-4x + 8| ≥ 2, which of the following statements is correct?a)No value of x satisfies this inequalityb)0 < x ≤ 3/2 or x ≥ 5/2c)3/2 ≤ x ≤ 5/2d)|x| > 1e)x|x| < 4Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice GMAT tests.
|
|
Explore Courses for GMAT exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup