91Ó°ÊÓ

When you're solving linear equations, the goal is to isolate the variable, making it easier to find its value. The subtraction property of equality is a handy tool to achieve this.
It tells us that we can subtract the same number from both sides of an equation without changing the equation's balance. Let's look at our example: - The equation begins as: \( 0.06y + 2.63 = 2.5562 \)- To start isolating the variable term \(0.06y\), we subtract \(2.63\) from both sides of the equation.- This gives us: \( 0.06y + 2.63 - 2.63 = 2.5562 - 2.63 \)- Simplifying, we get: \( 0.06y = -0.0738 \)By applying the subtraction property of equality, we eliminate the constant term on the left side, bringing us closer to isolating \(y\). Remember, whatever you do to one side, you must do to the other, maintaining equality.

After isolating the variable term with subtraction, the next step is to actually solve for the variable. That's where the division property of equality comes in.This property assures us that we can divide both sides of an equation by the same non-zero number, and the equation will stay balanced.Here's how it works in our example:- We have the equation: \( 0.06y = -0.0738 \)- To solve for \(y\), divide both sides by \(0.06\): \( y = \frac{-0.0738}{0.06} \)- After performing the division, we find: \( y = -1.23 \)Using division allows us to solve for \(y\). Just like subtraction, we must treat both sides equally. Dividing by the coefficient of \(y\) simplifies it to \(1y\), leaving just the variable on one side.

Simplifying equations is crucial as it transforms the equation into a more workable form before solving. It involves reducing complex expressions into simpler ones.In our initial steps, simplification came into play after employing the subtraction property:- The equation was simplified from: \( 0.06y + 2.63 - 2.63 = 2.5562 - 2.63 \) which results in: \( 0.06y = -0.0738 \)You'll notice the equation is easier to work with. After the division property, simplification again confirms the calculated value:- We divided the simplified equation: \( y = \frac{-0.0738}{0.06} \) becoming: \( y = -1.23 \)The entire process reflects simplifying intricate expressions at each stage to make solving the equation straightforward and efficient. Equations are like puzzles, the simpler pieces are easier to fit together, leading directly to the solution.