Solve for all values of yy in simplest form.
open vertical bar, 13, minus, 2, y, close vertical bar, equals, 19
∣13−2y∣=
19

We are given the equation:

\[
|13 - 2y| = 19
\]

To solve for \( y \), we need to consider the two possible cases for the absolute value equation. The absolute value expression \( |13 - 2y| = 19 \) implies two possible equations:

### Case 1:
\[
13 - 2y = 19
\]

Solving for \( y \):
\[
13 - 2y = 19 \quad \Rightarrow \quad -2y = 19 - 13 \quad \Rightarrow \quad -2y = 6 \quad \Rightarrow \quad y = \frac{6}{-2} \quad \Rightarrow \quad y = -3
\]

### Case 2:
\[
13 - 2y = -19
\]

Solving for \( y \):
\[
13 - 2y = -19 \quad \Rightarrow \quad -2y = -19 - 13 \quad \Rightarrow \quad -2y = -32 \quad \Rightarrow \quad y = \frac{-32}{-2} \quad \Rightarrow \quad y = 16
\]

Thus, the two solutions are:
\[
y = -3 \quad \text{or} \quad y = 16
\]

Do you have any questions or would you like more details?

Here are 5 related questions:
1. How do you solve absolute value inequalities?
2. What are the properties of absolute values?
3. How do you graph absolute value functions?
4. Can absolute values be negative?
5. How do you solve absolute value equations with multiple variables?

**Tip:** Always consider both the positive and negative scenarios when solving absolute value equations.

Solve for all values of y in simplest form. |13 - 2y| = 19

Learn how to solve the absolute value equation |13 - 2y| = 19 with a detailed step-by-step solution. This problem covers key algebraic concepts and properties of absolute values. Suitable for students in Grades 8-10.

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