91Ó°ÊÓ

When solving linear equations, one of the key steps is isolating the variable. This means getting the variable you are solving for on one side of the equation by itself. In the given exercise, we start with the equation:
\(10 x + 4 = 9 x\).
The goal is to get all the terms involving x on one side. We can do this by performing operations that simplify the equation and move terms around.
For example, we need to subtract 9x from both sides:
\(10 x + 4 - 9 x = 9 x - 9 x\).
This gives us:
\(x + 4 = 0\).
Now, x is on one side by itself but we need to get rid of the 4. We do this by subtracting 4 from both sides:
\(x + 4 - 4 = 0 - 4\).
This simplifies to:
\(x = -4\).
By following these steps, we have isolated the variable x.

Simplifying an equation is a crucial step in solving it. This involves combining like terms and performing arithmetic operations to make the equation easier to work with. Let's look at our initial equation again:
\(10 x + 4 = 9 x\).
Before we can isolate the variable, we need to simplify the equation by moving all terms involving x to one side.
We do this by subtracting 9x from both sides:
\(10 x + 4 - 9 x = 9 x - 9 x\).
This results in:
\(x + 4 = 0\).
Now the equation is much simpler and we can easily isolate x.
Remember, simplifying each step makes the equation easier to solve.

Solving linear equations involves a series of basic algebra steps. Here’s a quick summary:

• Identify the terms with the variable on both sides of the equation.
• Move all variable terms to one side by adding or subtracting them from both sides.
• Combine like terms if needed.
• Simplify the resulting equation.
• Isolate the variable by performing the appropriate arithmetic operations.

In our example, we started with:
\(10 x + 4 = 9 x\).
We moved the variable terms to one side:
\(10 x + 4 - 9 x = 9 x - 9 x\),
which gave us:
\(x + 4 = 0\).
Finally, we isolated x by subtracting 4 from both sides:
\(x = -4\).
Following these steps systematically ensures that you can solve any linear equation effectively.