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Math  /  Numbers & Operations

QuestionQuestion
Plot 3 and -7 on the number line below.
Find the distance between 3 and -7 .
Answer Attempt 2 out of 2 □\square units Snbmit Answer

Studdy Solution

STEP 1

1. We are working with real numbers and the number line.
2. The distance between two points on the number line is the absolute value of the difference between the numbers.
3. The given points are 3 and -7.

STEP 2

1. Identify the positions of the numbers 3 and -7 on the number line.
2. Use the formula for the distance between two points on the number line.

STEP 3

Identify the position of the number 3 on the number line. The number 3 is located three units to the right of 0.

STEP 4

Identify the position of the number -7 on the number line. The number -7 is located seven units to the left of 0.

STEP 5

Use the formula for the distance between two points on the number line:
Distance=∣a−b∣ \text{Distance} = |a - b|
where a a and b b are the two points on the number line.

STEP 6

Plug in the values a=3 a = 3 and b=−7 b = -7 into the formula:
Distance=∣3−(−7)∣ \text{Distance} = |3 - (-7)|

STEP 7

Simplify the expression inside the absolute value:
Distance=∣3+7∣ \text{Distance} = |3 + 7|

STEP 8

Evaluate the expression:
Distance=∣10∣ \text{Distance} = |10|

STEP 9

Since the absolute value of 10 is 10:
Distance=10 \text{Distance} = 10
The distance between 3 and -7 on the number line is 10 10 units.

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