To solve the equation \(|x + 10| = 23\), we need to consider the definition of absolute value. Absolute value measures the distance of a number from zero on the number line, so \(|x + 10|\) can equal 23 in two scenarios:

1. \(x + 10 = 23\)
2. \(x + 10 = -23\)

Let's solve both equations:

### 1. \(x + 10 = 23\)

Subtract 10 from both sides:

\[
x = 23 - 10
\]

\[
x = 13
\]

### 2. \(x + 10 = -23\)

Subtract 10 from both sides:

\[
x = -23 - 10
\]

\[
x = -33
\]

### Solution
The solutions are:

\[
x = 13 \quad \text{and} \quad x = -33
\]

Would you like more details or have any questions? Here are some related questions:

1. How do you solve other absolute value equations like \(|2x - 5| = 10\)?
2. What happens when the equation inside the absolute value is a quadratic?
3. How do absolute value inequalities differ from absolute value equations?
4. What are the graphical interpretations of absolute value functions?
5. How does the absolute value function affect transformations of graphs?

**Tip:** When solving absolute value equations, always split into two separate equations to handle the positive and negative scenarios.

Learn how to solve the absolute value equation |x + 10| = 23 with a clear, step-by-step solution. This algebraic problem highlights key concepts such as absolute value properties and solving linear equations. Suitable for students in Grades 7-9.

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