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\(-4\leq{x}\leq{7}\) from the image. From A we know that the distance between x and 1,5 is 5,5( in both ways) so x ranges from 7 and -4. Correct A
_________________

It is beyond a doubt that all our knowledge that begins with experience.

\(-4\leq{x}\leq{7}\) from the image. From A we know that the distance between x and 1,5 is 5,5( in both ways) so x ranges from 7 and -4. Correct A

i could not be able to understand. Can you/someone explain more.

Try solving the mod equation if you are confused.

As per the image we can see that −4≤x≤7

(A) |x − 1.5| ≤ 5.5 ===> -5.5 ≤ x - 15 ≤ 5.5 ==> -4 ≤ x ≤ 7 - This is exactly matching to the above equation. (B) |x + 5.5| ≥ 1.5 (C) |x + 1.5| ≤ 5.5 (D) |x − 5.5| ≤ 1.5 (E) |x − 1.5| ≥ 5.5

Though you can still do a quick check on rest of the answer choices. Hope this helps.

Hence, Answer is A _________________

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I got the answer right, but I had a hard time telling from the diagram whether the lower and upper limits were -4.5 and 7.5 (which it still looks like to me), or -4 and 7.