https://file.aiquickdraw.com/mathbot/file/1725926208423hgu70f8w.jpg

The equation given in the image is:

\[
|x + 1| = 6
\]

To solve this absolute value equation, we break it into two cases:

### Case 1: \( x + 1 = 6 \)
Solve for \( x \):

\[
x = 6 - 1 = 5
\]

### Case 2: \( x + 1 = -6 \)
Solve for \( x \):

\[
x = -6 - 1 = -7
\]

Thus, the two solutions are:

\[
x = 5 \quad \text{or} \quad x = -7
\]

Let me know if you'd like further details or have any questions!

Here are 5 related questions for practice:
1. Solve \( |x - 3| = 8 \).
2. Solve \( |2x + 4| = 10 \).
3. What does the graph of \( |x + 1| \) look like?
4. Solve \( |x - 5| = 0 \).
5. What happens if the right side of the absolute value equation is negative, like \( |x + 1| = -2 \)?

**Tip:** When solving absolute value equations, remember to always consider both the positive and negative cases!

Learn how to solve the absolute value equation |x + 1| = 6 step by step. This example demonstrates how to break an absolute value equation into two cases: positive and negative. Explore key algebraic concepts such as absolute value and solving linear equations, suitable for students in Grades 7-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation