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The distributive property is a key concept in solving linear equations. It allows you to distribute a number across terms inside parentheses. For example, in the equation \(5(w+2.2)-4 w=9.3\), you apply the distributive property to the term \(5(w + 2.2)\). Here's how it works:

Multiply 5 by both \(w\) and \(2.2\). So, you get:

\(5(w) + 5(2.2)\)

This simplifies to:

\(5w + 11\)

Now, substitute back into the original equation to get:

\(5w + 11 - 4w = 9.3\)

By distributing the 5, you have broken down the equation into simpler parts.

Combining like terms is another important step in solving linear equations. Like terms are terms that contain the same variables raised to the same power. In our equation:

\(5w + 11 - 4w = 9.3\)

Notice that \(5w\) and \(-4w\) are like terms because they both contain the variable \(w\). Combine them to simplify the equation further:

\(5w - 4w\)

This simplifies to:

\(w\)

So now the equation is:

\(w + 11 = 9.3\)

Combining like terms makes the equation easier to handle by reducing its complexity.

The final step in solving the equation is isolating the variable. This means getting the variable (in this case, \(w\)) by itself on one side of the equation. Starting with:

\(w + 11 = 9.3\)

To isolate \(w\), we need to get rid of the \(+ 11\). We do this by performing the opposite operation. Since 11 is added, we will subtract 11 from both sides. This maintains the balance of the equation. Let's see it step by step:

Subtract 11 from both sides:

\(w + 11 - 11 = 9.3 - 11\)

Simplify the equation:

\(w = -1.7\)

Now, the variable \(w\) is isolated, and we've found the solution: \(w = -1.7\)

Isolating the variable helps you find the value of the unknown, solving the equation completely.