https://file.aiquickdraw.com/mathbot/file/17260218527177f8uvavo.jpg

The equation given in the image is:

\[
\frac{9}{4}y - 12 = \frac{1}{4}y - 4
\]

### Step-by-step solution:

1. **Move all terms involving \( y \) to one side**:
   Subtract \( \frac{1}{4}y \) from both sides:

   \[
   \frac{9}{4}y - \frac{1}{4}y - 12 = -4
   \]

   Simplify the left-hand side:

   \[
   \frac{8}{4}y - 12 = -4
   \]

   This simplifies to:

   \[
   2y - 12 = -4
   \]

2. **Move constant terms to the other side**:
   Add 12 to both sides:

   \[
   2y = -4 + 12
   \]

   Simplify:

   \[
   2y = 8
   \]

3. **Solve for \( y \)**:
   Divide both sides by 2:

   \[
   y = \frac{8}{2}
   \]

   \[
   y = 4
   \]

### Final Answer:
\[
y = 4
\]

Would you like a deeper explanation or have any questions on any step?

Here are 5 related questions to practice:

1. Solve: \( \frac{5}{3}y - 7 = \frac{2}{3}y + 5 \)
2. Solve: \( \frac{7}{2}x + 10 = \frac{1}{2}x + 16 \)
3. Solve: \( \frac{3}{5}y - 4 = \frac{1}{5}y + 1 \)
4. Solve: \( \frac{6}{7}y + 8 = \frac{2}{7}y + 12 \)
5. Solve: \( 2y - 5 = 3y + 2 \)

**Tip**: Always simplify the equation by isolating terms involving the variable on one side and constants on the other side.

Learn how to solve the linear equation (9/4)y - 12 = (1/4)y - 4 with a step-by-step solution. This problem covers key algebraic concepts, including combining like terms and isolating the variable. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation