Final answer:
To rewrite |10 - x| without absolute value bars, one must consider the value of x. If x ≤ 10, the expression is (A) 10 - x; if x > 10, the expression is (C) x - 10.
Step-by-step explanation:
To rewrite |10 - x| without absolute value bars, we need to consider two cases because the absolute value of a number is the non-negative value of that number without regard to its sign. It ensures that whatever the number inside the absolute value bracket is, the result is always non-negative. If the value inside the absolute value, which is 10 - x, is non-negative (meaning x ≤ 10), then the expression without the absolute value bars is simply 10 - x. However, if the value inside is negative (meaning x > 10), the expression without the absolute value bars is -(10 - x) or x - 10, because we must negate it to make it non-negative.
The correct answer, therefore, depends on the value of x. For x ≤ 10, you would use answer (A) 10 - x, and for x > 10, you would use answer (C) x - 10. The other options provided, (B) -(10 - x) and (D) -(x - 10), represent the negated versions of (A) and (C) respectively but do not reflect the non-negative result of the absolute value when x ≤ 10.