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To solve the given linear equation, we start by isolating the variable. The variable in this case is x. We need to move everything else to the other side of the equation to get x by itself. Let's look at the initial equation, which is \( -7 = x - 22 \). Our goal is to leave x alone on one side. We do this by performing the opposite operation of what is currently being done to x. Right now, x is being subtracted by 22. To undo this, we add 22 to both sides of the equation.

Here are the steps:

• Original equation: \( -7 = x - 22 \)
• Add 22 to both sides: \( -7 + 22 = x - 22 + 22 \)
• Simplify both sides: \( 15 = x \)

Now, x is isolated, and we find that \( x = 15 \). This process is crucial in solving linear equations because it helps us find the value of the variable.

After isolating the variable and finding a solution, the next essential step is to verify the solution. This ensures that our solution is correct and satisfies the original equation. Let's verify our solution for the equation \( -7 = x - 22 \). We found that \( x = 15 \). To verify it, we substitute \(x = 15 \) back into the original equation.

• Original equation: \( -7 = x - 22 \)
• Substitute \( x = 15 \): \( -7 = 15 - 22 \)
• Simplify the right side: \( 15 - 22 = -7 \)
• Both sides are equal: \( -7 = -7 \)

Since both sides of the equation match, our solution \( x = 15 \) is indeed correct. Verifying solutions helps to ensure that we have not made any mistakes in our calculations.

Solving linear equations involves a series of fundamental algebraic steps. Here, we break down these steps using our sample problem to make it clear:

1. **Understand the equation**: Identify what is being asked and what needs to be solved. In our problem, we started with \( -7 = x - 22 \), and we needed to solve for x.
2. **Isolate the variable**: Perform operations to get the variable alone on one side of the equation. We added 22 to both sides to cancel out the \( -22 \).
3. **Simplify**: Combine like terms to simplify the equation. After adding 22 to both sides, we simplified to get \( 15 = x \).
4. **Verify the solution**: Substitute the solution back into the original equation to check if it holds true. By substituting \( x = 15 \) back into \( -7 = x - 22 \), we confirmed that both sides equaled -7.

These basic algebra steps provide a consistent method for solving similar problems. By following these steps, you can confidently solve linear equations and verify your solutions.