The numbers that are a distance of 7 units from -2 on a number line are 5 and -9.
What is the distance between two points on the number line?
"It is the absolute value of the difference of their coordinates."
For given question,
We need to find the numbers that are a distance of 7 units from -2 on a number line.
Using the definition of distance between two points on the number line,
⇒ |x - (-2)| = 7
⇒ |x + 2| = 7
⇒ x + 2 = ± 7
⇒ x + 2 = 7 and x + 2 = -7
⇒ x = 7 - 2 and x = -7 - 2
⇒ x = 5 and x = -9
Therefore, the numbers that are a distance of 7 units from -2 on a number line are 5 and -9.
Learn more about the distance between two points on the number line here:
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