consider the equation 2x-7y=5. Solve the equation for x in terms of y.

To solve the equation \( 2x - 7y = 5 \) for \( x \) in terms of \( y \), follow these steps:

1. Start with the original equation:
   \[
   2x - 7y = 5
   \]

2. Isolate \( 2x \) by adding \( 7y \) to both sides:
   \[
   2x = 7y + 5
   \]

3. Divide both sides of the equation by 2 to solve for \( x \):
   \[
   x = \frac{7y + 5}{2}
   \]

Thus, the solution for \( x \) in terms of \( y \) is:
\[
x = \frac{7y + 5}{2}
\]

Would you like a more detailed explanation, or do you have any questions about the steps?

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Here are 5 related questions to explore:

1. What would the value of \( x \) be if \( y = 2 \)?
2. How can you rewrite the equation \( 2x - 7y = 5 \) in slope-intercept form?
3. How would you solve for \( y \) in terms of \( x \) from the equation \( 2x - 7y = 5 \)?
4. What is the significance of the slope of the equation in a linear graph?
5. If the equation were instead \( 2x - 7y = 10 \), how would the solution for \( x \) change?

**Tip:** When solving linear equations, isolating one variable first can simplify the process greatly.

Consider the equation 2x - 7y = 5. Solve the equation for x in terms of y.

Learn how to solve the linear equation 2x - 7y = 5 for x in terms of y with a clear, step-by-step solution. This algebra problem demonstrates key concepts such as isolating variables and solving linear equations. Suitable for students in Grades 8-10.

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