To solve for \( y \) in the equation:

\[
|6 - 3y| = 1
\]

we need to consider both cases, as absolute values can represent either positive or negative results:

### Case 1: \( 6 - 3y = 1 \)
1. Subtract \( 6 \) from both sides:
   \[
   -3y = -5
   \]
2. Divide by \( -3 \):
   \[
   y = \frac{5}{3}
   \]

### Case 2: \( 6 - 3y = -1 \)
1. Subtract \( 6 \) from both sides:
   \[
   -3y = -7
   \]
2. Divide by \( -3 \):
   \[
   y = \frac{7}{3}
   \]

### Solution
The values of \( y \) that satisfy the equation are:
\[
y = \frac{5}{3} \quad \text{or} \quad y = \frac{7}{3}
\]

Would you like more details or have any questions?

---

1. How does absolute value affect equation solutions?
2. What other steps are needed for solving absolute value inequalities?
3. How would this solution change if it were \( |6 - 3y| = -1 \)?
4. What if \( |6 - 3y| = 0 \)? How many solutions would there be?
5. How can this method be used for complex expressions inside absolute values?

**Tip:** Always check both cases in absolute value equations for complete solutions.

Discover how to solve the absolute value equation |6 - 3y| = 1 with a clear, step-by-step explanation. This solution covers essential algebraic concepts and absolute value properties, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation