Question

When x < 0, |x - 7| is equivalent to which expression?

A. 7 - x
B. x - 7
C. 7 + x
D. 7 - |x|

Answer 1

For x < 0, the expression |x - 7| is equivalent to 7 - x since the absolute value of a negative value negates the sign, thus turning x - 7 into its positive counterpart.

Step-by-step explanation:

When x is less than 0, the expression |x - 7| is equivalent to the expression 7 - x. This is because the absolute value function outputs the distance of a number from zero on the number line, without regard to direction. Since x is negative, x - 7 will also be negative, and the absolute value function will change the sign to make it positive. Thus, the equivalent expression when x < 0 is 7 - x.