Question

(a) use the number line to find the distance between -1 and 7.

distance:

(b) find the differences involving -1 and 7 below.
-1 - 7 =
7 - (-1) =

(c) find the absolute value of each difference.
|-1 - 7| =
|7 - (-1)| =

Explanation:

Step1: Count units between -1 and 7

On the number line, from -1 to 0 is 1 unit, 0 to 7 is 7 units. Total: $1 + 7 = 8$

Step2: Calculate $-1 -7$

Subtract 7 from -1: $-1 - 7 = -8$

Step3: Calculate $7 - (-1)$

Subtract negative 1 (add 1): $7 + 1 = 8$

Step4: Find $|-1 -7|$

Take absolute value of -8: $|-8| = 8$

Step5: Find $|7 - (-1)|$

Take absolute value of 8: $|8| = 8$

Answer:

(a) 8
(b) $-1 -7 = -8$; $7 - (-1) = 8$
(c) $|-1 -7| = 8$; $|7 - (-1)| = 8$