Solve for all values of y*y* in simplest form.

open vertical bar, 6, minus, 3, y, close vertical bar, equals, 1

∣6−3*y*∣=

1

To solve the equation \(\left|6 - 3y\right| = 1\), we again need to consider both possible cases of the absolute value expression.

Given the equation \(\left|6 - 3y\right| = 1\), this means:

1. \(6 - 3y = 1\)
2. \(6 - 3y = -1\)

We will solve each case separately.

### Case 1: \(6 - 3y = 1\)

\[
6 - 3y = 1
\]

Subtract 6 from both sides:

\[
-3y = -5
\]

Now, divide both sides by \(-3\):

\[
y = \frac{5}{3}
\]

### Case 2: \(6 - 3y = -1\)

\[
6 - 3y = -1
\]

Subtract 6 from both sides:

\[
-3y = -7
\]

Now, divide both sides by \(-3\):

\[
y = \frac{7}{3}
\]

### Final Solution

The solutions to the equation are \(y = \frac{5}{3}\) and \(y = \frac{7}{3}\).

Would you like any further details or have any questions?

Here are 5 related questions:
1. What would the solutions be if the equation were \(\left|2 - y\right| = 3\)?
2. How can we check if the solutions obtained are correct?
3. What would be the impact on the solutions if the absolute value expression was \(\left|6 - 3y\right| = 0\)?
4. How would the solution process differ if there were additional terms on both sides, like \(\left|6 - 3y\right| = y + 1\)?
5. What is the geometric interpretation of solving an absolute value equation like this?

**Tip:** Always double-check your solutions by substituting them back into the original equation to ensure they satisfy the equation.

Learn how to solve the absolute value equation |6 - 3y| = 1 step-by-step with detailed solutions. Understand the concepts of absolute value and linear equations. Suitable for Grades 7-9 students.

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