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The equation provided is \( y = mx + b \), and we are asked to solve for \( x \).

### Step-by-step solution:

1. Start with the equation:
   \[
   y = mx + b
   \]

2. Subtract \( b \) from both sides to isolate the \( mx \) term:
   \[
   y - b = mx
   \]

3. Now, divide both sides by \( m \) to solve for \( x \):
   \[
   x = \frac{y - b}{m}
   \]

Thus, the solution for \( x \) is:
\[
x = \frac{y - b}{m}
\]

Would you like further clarification or more details on any steps?

Here are five related questions to explore further:
1. How would the solution change if \( m = 0 \)?
2. Can you explain the geometric interpretation of the equation \( y = mx + b \)?
3. What happens to \( x \) if \( y = b \)?
4. How do you solve the equation if both \( m \) and \( b \) are unknown?
5. How does this equation relate to the slope-intercept form of a linear equation?

**Tip:** When solving for a variable, always aim to isolate the variable on one side by using inverse operations, like addition, subtraction, multiplication, or division.

Learn how to solve for x in the linear equation y = mx + b with a detailed step-by-step guide. This problem covers key algebra concepts, including isolating the variable x and applying inverse operations. Suitable for students in Grades 8-10.

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