Question

Compare numbers to their opposites based on their positions on a number line. Choose ALL true statements based on these comparisons.

A) −(−7) = 7
B) Zero is its own opposite.
C) −(−10) = −10
D) −14 and 4 are equally distant from 0.
E) −12 and 12 are equally distant from 0.

Answer 1

The true statements when comparing numbers and their opposites on a number line are that -(-7) = 7, zero is its own opposite, and -12 and 12 are equally distant from zero. Statements A, B, and E are correct.

Step-by-step explanation:

The question involves comparing numbers and their opposites on a number line, which is a fundamental concept in mathematics.

• A) −(−7) = 7 is true because the opposite of -7 is 7.
• B) Zero is its own opposite, which is also true because zero is in the middle of the number line and does not have a positive or negative sign.
• C) −(−10) = −10 is false because the opposite of -10 is 10, not -10.
• D) −14 and 4 are not equally distant from 0, this statement is false.
• E) −12 and 12 are equally distant from 0, which is true because they are on the opposite sides of zero on the number line and at the same distance.

The correct answers are A, B, and E.

Answer 2

E is one answer because 12 and -12 are absolute values.