the numbers represented by variables a and c , on the number line, are integers.
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a c
If , under which of the following conditions could the expression be true?
A.when a=-5 and c=5
B.when a=0 andc=10
C.whena=7 and c=3
D.when a=-6 and c=-1
To answer this question, we need to understand the relationship between the variables a and c, and determine which conditions would make the expression (a < c) true.
In option A, when a = -5 and c = 5, since -5 is less than 5, the expression (a < c) is true.
In option B, when a = 0 and c = 10, since 0 is less than 10, the expression (a < c) is true.
In option C, when a = 7 and c = 3, since 7 is greater than 3, the expression (a < c) is false.
In option D, when a = -6 and c = -1, since -6 is less than -1, the expression (a < c) is true.
Therefore, the conditions under which the expression (a < c) is true are option A (when a = -5 and c = 5), option B (when a = 0 and c = 10), and option D (when a = -6 and c = -1).
So, the correct answer would be options A, B, and D.
The expression |a - c| < 6 represents the absolute difference between variables a and c being less than 6. We can evaluate each option to see which one satisfies this condition.
A. when a=-5 and c=5:
|a - c| = |-5 - 5| = |-10| = 10
The absolute difference between -5 and 5 is 10 which is not less than 6. Therefore, option A does not satisfy the condition.
B. when a=0 and c=10:
|a - c| = |0 - 10| = |-10| = 10
The absolute difference between 0 and 10 is 10 which is not less than 6. Therefore, option B does not satisfy the condition.
C. when a=7 and c=3:
|a - c| = |7 - 3| = |4| = 4
The absolute difference between 7 and 3 is 4, which is less than 6. Therefore, option C satisfies the condition.
D. when a=-6 and c=-1:
|a - c| = |-6 - (-1)| = |-6 + 1| = |-5| = 5
The absolute difference between -6 and -1 is 5, which is less than 6. Therefore, option D satisfies the condition.
Therefore, the conditions under which the expression |a - c| < 6 is true are options C and D.