91Ó°ÊÓ

When solving linear equations, the first step is often to combine like terms. Like terms are terms in an equation that have the same variable raised to the same power. In our exercise, we have two terms on the left side of the equation: \(0.8m + 0.05m\). Here, both terms are like terms because they both contain the variable \(m\).

To combine them, you simply add the coefficients (the numbers in front of the variables). In this case, add \(0.8\) and \(0.05\) to get \(0.85\). This simplifies our equation to \(0.85m = 0.34\).

Thus, combining like terms helps to simplify the equation, making the next steps of solving much easier.

Always check for like terms and combine them to maintain a clear and simple equation as we progress through solving it.

After we have combined like terms, the next step is to isolate the variable. Isolating the variable means getting the variable (in this case, \(m\)) alone on one side of the equation.

In our example, our simplified equation is \(0.85m = 0.34\). To isolate \(m\), we need to get rid of the coefficient (\(0.85\)) that is multiplying \(m\).

To do that, we use the inverse operation. Since \(0.85\) is multiplying \(m\), we will divide both sides of the equation by \(0.85\). This gives us:
\[m = \frac{0.34}{0.85}\]

Now, \(m\) is isolated, and we can see the solution clearly.

Isolating the variable is a crucial step because it helps us to see the solution directly and understand how the variable relates to the values in the equation.

Division in algebra is an important tool to solve equations, especially when we are isolating a variable. When we have an equation where a variable is multiplied by a coefficient, we use division to move the coefficient to the other side of the equation.

In our problem, to isolate \(m\), we divided both sides of the equation by \(0.85\). Remember that whatever operation you do to one side of the equation, you must do to the other to keep the equation balanced. So, from \(0.85m = 0.34\), we get:

\[m = \frac{0.34}{0.85} = 0.4\]

This means that \(m\) equals \(0.4\).

Division in algebra helps to simplify expressions and solve for variables. Always ensure that you perform the division correctly and keep the equation balanced. This ensures accuracy in finding the solution.