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03 Jul 2024, 23:12
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D
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Difficulty:
5%
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Question Stats:
99% (00:28) correct
1%
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wrong
based on 376
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If x is positive and the distance between -7 and 0 is equal to the distance between x and 0, what is the value of x?
A. 1
B. 3
C. 5
D. 7
E. 9
A. 1
B. 3
C. 5
D. 7
E. 9
03 Jul 2024, 23:38
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sahilsah456
The distance between -7 and 0 is equal to the distance between x and 0:
|7 - 0| = |x - 0|
|7| = |x|
Since, x > 0, then |x| = x thus:
7 = x
Answer: D.
11 Oct 2024, 09:31
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Given that x is positive and the distance between -7 and 0 is equal to the distance between x and 0 and We need to find x
Let's solve the problem using two methods
Method 1: Algebra
Distance of a number from another number = Absolute value of the difference between those number
=> Distance between -7 and 0 = Distance between x and 0
=> Absolute difference between -7 and 0 = Absolute difference between x and 0
=> | -7 - 0| = | x - 0|
=> |-7| = |x|
Now, x is +ve => |x| = x
=> 7 = x or x = 7
Method 2: Substitution
Distance between -7 and 0 = 7. Lets take each option choice and see whose distance from 0 will be 7
A. 1, Distance between 0 and 1 = 1 ≠ 7 => FALSE
B. 3, Distance between 0 and 3 = 3 ≠ 7 => FALSE
C. 5, Distance between 0 and 5 = 5 ≠ 7 => FALSE
D. 7, Distance between 0 and 7 = 7 => TRUE
E. 9, Distance between 0 and 9 = 9 ≠ 7 => FALSE
So, Answer will be D
Hope it helps!
Playlist on Solve problems on Absolute Value here
Watch the following video to MASTER Absolute Values
Let's solve the problem using two methods
Method 1: Algebra
Distance of a number from another number = Absolute value of the difference between those number
=> Distance between -7 and 0 = Distance between x and 0
=> Absolute difference between -7 and 0 = Absolute difference between x and 0
=> | -7 - 0| = | x - 0|
=> |-7| = |x|
Now, x is +ve => |x| = x
=> 7 = x or x = 7
Method 2: Substitution
Distance between -7 and 0 = 7. Lets take each option choice and see whose distance from 0 will be 7
A. 1, Distance between 0 and 1 = 1 ≠ 7 => FALSE
B. 3, Distance between 0 and 3 = 3 ≠ 7 => FALSE
C. 5, Distance between 0 and 5 = 5 ≠ 7 => FALSE
D. 7, Distance between 0 and 7 = 7 => TRUE
E. 9, Distance between 0 and 9 = 9 ≠ 7 => FALSE
So, Answer will be D
Hope it helps!
Playlist on Solve problems on Absolute Value here
Watch the following video to MASTER Absolute Values
