91Ó°ÊÓ

In linear equations, the first step often involves combining like terms. This means rearranging the equation so all terms involving the variable are on one side, and the constant terms are on the other side. For our example, we start with:$$ -3.48x + 6.981 = 4.329x - 6.851 $$Add \(3.48x\) to both sides to move all \(x\) terms to one side:$$ -3.48x + 3.48x + 6.981 = 4.329x + 3.48x - 6.851 $$Notice how the \( -3.48x\) and the \( +3.48x\) on the left side cancel out, leaving:$$ 6.981 = 7.809x - 6.851 $$Next, add \(6.851\) to both sides to move constant terms to the right:$$ 6.981 + 6.851 = 7.809x - 6.851 + 6.851 $$Again, the \( -6.851\) and \( +6.851\) cancel out, simplifying to:$$ 13.832 = 7.809x $$Combining like terms helps simplify the equation, making it easier to isolate the variable.

Once like terms are combined, the next step is isolating the variable. This means getting the variable by itself on one side of the equation. Using our simplified equation:$$ 13.832 = 7.809x $$To isolate \(x\), divide both sides of the equation by \(7.809\):$$ x = \frac{13.832}{7.809} $$By performing this division, we are essentially 'undoing' the multiplication. Remember, the goal is to have \(x\) alone on one side, which makes solving for \(x\) straightforward. The equation now becomes:$$ x = \frac{13.832}{7.809} $$Dividing both sides is a vital step when isolating the variable, especially when coefficients involve decimals.

The final step is performing the division to find the value of \(x\). We use the equation:$$ x = \frac{13.832}{7.809} $$Using a calculator or performing the division by hand will give you the precise value of \( x \). The result is approximately:$$ x \approx 1.771 $$It’s important to remember to round to a reasonable number of decimal places, depending on the context of the problem. In many cases, two or three decimal places are suitable. Performing the division correctly ensures accurate final results for your solution.