91Ó°ÊÓ

When we want to solve a linear equation, like \(-2.8m = -8.4\), our main goal is to find the value of the unknown variable, which is represented by \(*m*\) in this case.
The first step in solving for \(*m*\) is to isolate it. Isolating the variable means getting the variable by itself on one side of the equation. This is often done by performing the same mathematical operations on both sides of the equation.
In our example, we need to isolate \(*m*\). Right now, \(-2.8m\) is equal to \(-8.4\). We have to do something to both sides of the equation so that we end up with \(*m*\) by itself on one side.
Remember, the goal of isolating variables is to make the equation simpler and reveal the value of the unknown variable.

One common operation used to isolate variables is division. Division helps when a variable is multiplied by a number, as we see in the given equation \(-2.8m = -8.4\).
Since \(*m*\) is multiplied by \( -2.8 \), we can isolate it by dividing both sides of the equation by \( -2.8 \). This way, we are left with \(*m* = \frac{-8.4}{-2.8} \).
Dividing each side of an equation by the same number keeps the equation balanced. Think of it as sharing both sides equally.
In our equation, when we divide both sides by \( -2.8 \), the left-hand side simplifies to \(*m*\) and the right-hand side simplifies to \(\frac{-8.4}{-2.8} = 3 \).
Division in equations is a very powerful tool for isolating variables and solving linear equations.

After isolating the variable and performing the division, we often end up with an expression that needs to be simplified.
Simplifying the expression makes it easier to understand and provides the final answer in a clear form.
For example, once we divide \(\frac{-8.4}{-2.8}\), we need to simplify this fraction. Luckily, in this case, dividing \(-8.4\) by \(-2.8\) gives us a whole number: \(*3*\). So, our simplified right-hand side is \(3\).
Once simplified, the expression gives the final value of the variable: \(m = 3\).
Simplifying expressions helps bring clarity and conciseness to our solutions, making the final answers straightforward for everyone to understand.