Solve for all values of yy in simplest form.
open vertical bar, 4, y, minus, 10, close vertical bar, equals, 20
∣4y−10∣=
20

We are given the equation: 

\[
|4y - 10| = 20
\]

To solve this absolute value equation, we consider two cases: 

### Case 1: 
The expression inside the absolute value is positive or zero:

\[
4y - 10 = 20
\]

Solve for \(y\):

\[
4y = 20 + 10 = 30
\]
\[
y = \frac{30}{4} = 7.5
\]

### Case 2: 
The expression inside the absolute value is negative:

\[
4y - 10 = -20
\]

Solve for \(y\):

\[
4y = -20 + 10 = -10
\]
\[
y = \frac{-10}{4} = -2.5
\]

### Final Answer:
The solutions are:

\[
y = 7.5 \quad \text{or} \quad y = -2.5
\]

Would you like more details or have any questions?

### Relative questions:
1. How do we solve an absolute value inequality?
2. What happens when the absolute value equation involves variables on both sides?
3. How can absolute values affect quadratic equations?
4. What is the geometric interpretation of an absolute value?
5. Can you explain how absolute value functions graphically form a "V" shape?

### Tip:
Always remember that solving absolute value equations involves considering both the positive and negative cases of the expression inside the absolute value!

Solve for all values of y in simplest form: |4y - 10| = 20

Learn how to solve the absolute value equation |4y - 10| = 20 with a detailed step-by-step solution. This algebra problem covers key concepts related to absolute value equations, exploring both positive and negative cases. Suitable for students in Grades 8-10.

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