Question content area top

Part 1

Find the solution set for the equation.

StartAbsoluteValue x plus 3 EndAbsoluteValue equals 0x+3=0

Question content area bottom

Part 1

Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

The solution set is

StartSet nothing EndSet .enter your response here.

​(Use a comma to separate answers as​ needed.)

B.

The solution set is all real numbers.

C.

The solution set is

empty set∅

We are asked to solve the equation:

\[
|x + 3| = 0
\]

### Step-by-step Solution:

1. The absolute value of any number is always non-negative, meaning it is either positive or zero. The equation \( |x + 3| = 0 \) implies that the expression inside the absolute value must be exactly zero because the absolute value of any non-zero number is positive.
   
2. So, we set the expression inside the absolute value equal to 0:

   \[
   x + 3 = 0
   \]

3. Solving for \(x\):

   \[
   x = -3
   \]

Thus, the only solution is \( x = -3 \).

### Checking:
Substitute \( x = -3 \) back into the original equation:

\[
| -3 + 3 | = | 0 | = 0
\]

Since both sides are equal, the solution is correct.

### Answer Choices:
- A. The solution set is \( \{-3\} \).
- B. The solution set is all real numbers. **(Incorrect)**, as there is only one solution.
- C. The solution set is the empty set \( \emptyset \). **(Incorrect)**, as we found a solution.

### Correct Answer: 
**A. The solution set is \( \{-3\} \).**

Would you like more details or further explanation?

Here are some related questions to expand on this topic:
1. What happens if \( |x + 3| = 5 \)?
2. How would the solution change for \( |x - 4| = 0 \)?
3. What is the general approach to solving absolute value equations?
4. How does the graph of \( y = |x + 3| \) look?
5. Can absolute value equations ever have more than one solution?

**Tip:** When solving absolute value equations, remember to split the equation into cases only if the right-hand side is non-zero.

Find the solution set for the equation |x + 3| = 0 and select the correct choice from the given options.

Understand how to solve the absolute value equation |x + 3| = 0 with a detailed step-by-step solution. This problem demonstrates key algebraic concepts, including absolute value properties and equation solving techniques. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation