Question

The solution set of which of the following equations is the set of real numbers that are 5 units from -3?

1) | x + 5 | = -3
2) | x - 5 | = 3
3) | x + 5 | = 3
4) | x - 3 | = 5
5) | x + 3 | = 5

Answer 1

The correct answer is option 5, which is | x + 3 | = 5, representing the set of real numbers that are 5 units from -3. This equation has two solutions, x = 2 and x = -8.

Step-by-step explanation:

The solution set of the equation that represents the set of real numbers that are 5 units from -3 is given by the equation | x + 3 | = 5. This equation means that the distance between any solution for x and -3 on the number line is 5 units. Since absolute value represents distance without regard to direction, there are two solutions: one 5 units greater than -3 (which is 2), and one 5 units less than -3 (which is -8).

Mathematically, the equation | x + 3 | = 5 can be solved by considering two cases: x + 3 = 5 or x + 3 = -5. Solving for x in each case yields x = 2 and x = -8, respectively. So, the two numbers that are 5 units from -3 are 2 and -8, and this is why option 5 is the correct answer.