To solve the equation \( y = \sqrt{7} - 5x \) for \(x\) using the four-step rule, follow these steps:

### Step 1: Isolate the Square Root (or the Constant)
First, we aim to isolate the term involving \(x\).

\[
y = \sqrt{7} - 5x
\]

Subtract \(\sqrt{7}\) from both sides to move the constant to the left side:

\[
y - \sqrt{7} = -5x
\]

### Step 2: Solve for the Variable
Next, solve for \(x\) by isolating it on one side of the equation.

Divide both sides by \(-5\):

\[
x = \frac{y - \sqrt{7}}{-5}
\]

This simplifies to:

\[
x = \frac{\sqrt{7} - y}{5}
\]

### Step 3: Verify the Solution
To ensure the solution is correct, substitute \(x = \frac{\sqrt{7} - y}{5}\) back into the original equation and check if both sides are equal:

Substitute \(x\) into the original equation:

\[
y = \sqrt{7} - 5\left(\frac{\sqrt{7} - y}{5}\right)
\]

Simplify the right-hand side:

\[
y = \sqrt{7} - (\sqrt{7} - y)
\]

\[
y = y
\]

Since the equation holds true, the solution is correct.

### Step 4: State the Final Answer
The solution for \(x\) is:

\[
x = \frac{\sqrt{7} - y}{5}
\]

Would you like any further details or explanations?

Here are some related questions to consider:
1. How does the solution change if the equation was \(y = \sqrt{7} + 5x\)?
2. How would you graph \(x = \frac{\sqrt{7} - y}{5}\)?
3. What is the domain of the function \(x = \frac{\sqrt{7} - y}{5}\)?
4. How does this solution compare to solving \(y = \sqrt{7 - 5x}\)?
5. Can you derive the inverse of the function given \(y = \sqrt{7} - 5x\)?

**Tip:** When solving equations, always check your solution by substituting it back into the original equation to ensure it satisfies the equation.

Learn how to solve the equation y = √7 - 5x step-by-step with a detailed solution. This problem involves isolating variables and applying basic algebraic principles. Suitable for students in Grades 7-9.

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