91Ó°ÊÓ

When solving linear equations, it's important to make the equation as simple as possible. One way to do this is by combining like terms. These are terms that have the same variable raised to the same power. For example, in the expression \(4x - 5x\), both terms involve the variable \(x\), which makes them like terms.
By combining \(4x\) and \(-5x\), we are essentially adding their coefficients together. Here's step by step how you can think about it:

• Identify the like terms on the same side of the equation.
• Add or subtract the coefficients of these terms.

In our example, combining \(4x\) and \(-5x\) means calculating \(4 - 5\), which equals \(-1\). Therefore, we replace \(4x - 5x\) with \(-1x\).
After simplifying, the equation becomes \(-x = -3\), setting up an easier path to find the solution.

Once we have a simpler version of the equation where all like terms are combined, the next step is finding the value of the variable by isolating it. Isolating a variable means getting it by itself on one side of the equation. In our case, after combining like terms, we got \(-x = -3\).
To isolate \(x\), you need to "undo" or perform the opposite operation on both sides of the equation. What's opposite of having a negative sign in front of \(x\)? Dividing by \(-1\), so:

• Divide both sides of the equation by \(-1\).
• This cancels the negative sign on \(x\), making it just \(x\).

Applying this step, our equation becomes \(x = 3\). Now the variable \(x\) is isolated, giving us a clear solution to the equation.

Negative coefficients appear in many algebra problems, and handling them correctly is crucial. A coefficient is a number that multiplies a variable. In our equation, after combining like terms, we have \(-1x=-3\), where \(-1\) is a negative coefficient.
Dealing with negative coefficients can be tricky, but there's a straightforward approach:

• If you encounter a negative coefficient, think about dividing by its absolute value to make the variable positive.
• This operation does not change the equality, as long as you perform it on both sides of the equation.

In our final equation \(-x = -3\), by dividing both sides by \(-1\), the negative coefficient \(-1\) is removed, resulting in \(x = 3\). Thus, treating negative coefficients becomes a manageable task by rationally employing inverse operations.