Solve for all values of yy in simplest form.
open vertical bar, 3, y, minus, 14, close vertical bar, equals, 17
∣3y−14∣=
17

We are given the equation:

\[
|3y - 14| = 17
\]

To solve for \( y \), we need to consider two cases, because the absolute value equation splits into two possible linear equations:

### Case 1:
\[
3y - 14 = 17
\]
Solve for \( y \):
\[
3y = 17 + 14
\]
\[
3y = 31
\]
\[
y = \frac{31}{3}
\]

### Case 2:
\[
3y - 14 = -17
\]
Solve for \( y \):
\[
3y = -17 + 14
\]
\[
3y = -3
\]
\[
y = \frac{-3}{3} = -1
\]

### Solution:
The two solutions for \( y \) are:

\[
y = \frac{31}{3} \quad \text{or} \quad y = -1
\]

Would you like further clarification or details on any step?

### Related Questions:
1. How do you solve absolute value equations in general?
2. Can absolute value equations have no solution?
3. What is the geometric meaning of absolute value equations?
4. How do you handle absolute value inequalities?
5. How do you solve absolute value equations with variables on both sides?

### Tip:
Always remember to check both cases when solving absolute value equations, as the expression inside can be positive or negative.

Solve for all values of y in simplest form: |3y - 14| = 17

Learn how to solve the absolute value equation |3y - 14| = 17 with step-by-step explanations. This problem covers key algebraic concepts such as solving absolute value equations and applying the absolute value property. Suitable for students in Grades 8-10.

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