91Ó°ÊÓ

When solving linear equations, simplifying the equation by combining like terms is an essential first step. This makes the equation easier to handle. Like terms are terms that have the same variable raised to the same power. In our exercise, we have the terms

• \(-9x\)
• \(+x\)

These can be combined because they both have the variable \(x\). To combine them, you add or subtract their coefficients, the numerical parts in front of the variables. In this case:

• \(-9 + 1 = -8\)

Thus, combining the terms yields \(-8x\). Now, our new equation is simply \(-8x = -8\). This step simplifies the equation, making it easier to solve in the next steps.
Remember, always combine like terms before trying to solve for the variable. This is because it reduces the complexity of the equation, leading to fewer steps.

After combining like terms, the next step is to isolate the variable. Here, we want to solve for \(x\). The equation we have is \(-8x = -8\). To isolate \(x\), you perform operations that ensure \(x\) is alone on one side of the equation.In this example, we want to eliminate \(-8\) that is multiplied by \(x\). To do this, divide both sides of the equation by \(-8\). When you divide \(-8x\) by \(-8\), you get \(x\). Ensure you do the same operation to both sides to maintain equality:\[x = \frac{-8}{-8} = 1\].Now \(x\) is by itself, which means it has been isolated. Isolating the variable is pivotal in solving equations as it gives you the solution directly. Make sure to perform each step carefully to avoid any errors.

Checking the solution is the final and crucial step in the process of solving a linear equation. It not only confirms the correctness of the solution but also reinforces understanding through validation.To check if \(x = 1\) is correct, substitute this value back into the original equation:\(-9(1) + 1 = -8\).Simplify the left side:

• \(-9 \cdot 1 = -9\)
• \(-9 + 1 = -8\)

The equation stands true as \(-8\) on both sides. This confirms that \(x = 1\) is correct and ensures confidence in your solution. Always double-check your solution to prevent mistakes and deepen the understanding of the solving process.