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When solving linear equations, one key step often involves the distributive property. The distributive property allows you to multiply a single term by each term within a set of parentheses. This is useful for eliminating parentheses and simplifying expressions.

For example, in the equation: 5(w + 2.2) - 4w = 9.3

Using the distributive property, you multiply 5 by both w and 2.2, transforming the equation to:

5w + 11 - 4w = 9.3

Remember, the distributive property is only applicable when you have multiplication outside of the parentheses and an addition or subtraction operation inside. Learning to apply the distributive property correctly is fundamental in algebra and will simplify many types of equations.

After using the distributive property, the next step often involves combining like terms. Like terms are terms that have the same variable raised to the same power. Combining them means adding or subtracting their coefficients. This simplifies the equation and makes it easier to solve.

In our example, after distribution, we have:

5w + 11 - 4w = 9.3

Here, 5w and -4w are like terms. Combining them, 5w - 4w results in w. The equation now simplifies to:

w + 11 = 9.3

By mastering the skill of combining like terms, you can significantly simplify the steps involved in solving more complex equations.

The final step in many linear equations involves isolating the variable. Isolating the variable means getting the variable alone on one side of the equation. This can often be done through addition, subtraction, multiplication, or division.

In our example, the equation after combining like terms is:

w + 11 = 9.3

To isolate w, subtract 11 from both sides:

w + 11 - 11 = 9.3 - 11

Simplifying this, we get: w = -1.7

Now, the variable w is isolated. Isolating the variable is usually the final step in solving linear equations, allowing you to find the solution. Practicing this step often makes it easier to manage and solve equations effectively.