Question

The following picture shows a number line.

Each hash on the number line represents one unit. Which of the following statements is true?

A. The sum of points A, B, C, and D is greater than zero.

B. The sum of points B and C is greater than point A.

C. The sum of points A and B is greater than point C.

D. The opposite of point A is less than point D.
Show work here.

Answer 1

We conclude that only option B is true.

i.e. The sum of points B and C is greater than point A

Explanation:

Given the location of points on the left side of the number line

A=-6

B=-5

Given the location of points on the right side of the number line

C=3

D=4

Checking the statement A

The sum of points A, B, C, and D is greater than zero.

i.e. A+B+C+D > 0

-6 + -5 + 3 + 4 > 0

-11+7 > 0

-4 > 0

Thus,, this statement is false

Checking the statement B

The sum of points B and C is greater than point A

B+C>A

-5+3 > -6

-2 > -6

Thus, this statement is true.

Checking the statement C

The sum of points A and B is greater than point C

A+B > C

-6 + -5 > 3

-11 > 3

Thus, this statement is false

Checking the statement D

The opposite of point A is less than point D

As

A = -6

opposite of point A = -(-6)=6

The opposite of point A < D

6 < 4

Thus, this statement is false

Therefore, we conclude that only option B is true.

i.e. The sum of points B and C is greater than point A