Question

The distance between two numbers on a number line is 36. One of the numbers is 7. Write and solve an absolute value equation to find the two other possible numbers.

A. |x - 7| = 36; x = 43 or -29
B. |x + 7| = 36; x = 29 or -43
C. |x - 36| = 7; x = 43 or -29
D. |x + 36| = 7; x = 29 or -43

Answer 1

The correct absolute value equation to find two numbers that are 36 units away from the number 7 on a number line is |x - 7| = 36, which yields the solutions x = 43 and x = -29.

Step-by-step explanation:

The question asks us to find two numbers that are 36 units away from the number 7 on a number line, using an absolute value equation. The correct absolute value equation for this scenario would be |x - 7| = 36. To solve this equation, we must consider both the positive and negative solutions because absolute value signifies the distance from zero without considering direction.

To find the two possible solutions, we can set up two separate equations:

1. x - 7 = 36, which gives us x = 43
2. x - 7 = -36, which gives us x = -29

Therefore, the two numbers on the number line that are 36 units away from 7 are 43 and -29, corresponding to the positive and negative directions on the number line, respectively.