91Ó°ÊÓ

Isolating variables is a crucial step in solving linear equations, as it helps to find the value of the unknown variable. In our example, the equation is given as \( r - 8.6 = -8.1 \). Here, \( r \) is the variable we aim to isolate and solve for. To isolate the variable, we need to have it by itself on one side of the equation.
This often involves reversing operations that are currently applied to the variable. In this case, subtraction is involved, so we do the opposite - addition. We add \( 8.6 \) to both sides of the equation. By doing so, the \(-8.6\) and \(+8.6\) cancel one another on the left side, leaving only \( r \).
This gives us the simplified form \( r = ... \), successfully isolating the variable.

Checking solutions is a vital step to ensure accuracy. Once we have isolated the variable and solved for its value, we must verify our answer. This involves substituting the obtained solution back into the original equation.
In our case, after isolating \( r \), we found that \( r = 0.5 \). To check if this is correct, we substitute \( r = 0.5 \) back into the original equation: \( 0.5 - 8.6 = -8.1 \).
Calculate the left side to assure it equals the right side of the equation. Simplifying gives us \(-8.1 = -8.1\), which confirms our solution is correct and consistent with the equation. This step eliminates any errors and reinforces confidence in the solution.

Addition is a fundamental operation used to solve equations, especially when aiming to isolate a variable. In our problem, we began with \( r - 8.6 = -8.1 \). Subtraction was initially applied to \( r \), so we use addition to counteract this by adding \( 8.6 \) to both sides.
This process transforms the equation into \( r = 0.5 \), simplifying the task of solving for \( r \). Addition is applied to each side equally, maintaining balance and equality.

• This action cancels out terms.
• It brings terms to one side, aiding in isolation.

Using addition properly helps dissolve complex terms and work towards solving the equation straightforwardly and accurately.