Isolating variables in linear equations with subtraction is pretty simple. I learned this in Year 11, and I want to share some easy steps to help you understand it better. Here’s what you need to know:

Step 1: Know What a Linear Equation Looks Like

First, understand the structure of a linear equation.

It usually looks like this: $ax + b = c$.

In this format:

• $a$, $b$, and $c$ are numbers.
• $x$ is the variable, or the unknown value we want to find.

It’s important to know these parts because they guide what you do next.

Step 2: Find What to Subtract

Look closely at the equation to see which part is stopping you from isolating $x$.

This is usually a number added to $x$, which we call a constant (that’s the $b$).

For example, in the equation $3x + 4 = 10$, the $+4$ is what we need to get rid of.

Step 3: Subtract the Constant

Now, let’s use subtraction to isolate the variable.

You should subtract the constant from both sides of the equation.

In our example:

$$3x + 4 - 4 = 10 - 4$$

This simplifies to:

$$3x = 6$$

Remember: whatever you do to one side, do to the other side too!

Step 4: Simplify the Equation

After subtracting, see if you can simplify the equation further.

From the previous example, we have $3x = 6$.

This is much easier to work with!

Step 5: Isolate the Variable Completely

Next, we need to get $x$ all by itself.

Since $x$ is multiplied by $3$, we divide both sides by $3$:

$$x = \frac{6}{3}$$

So, $x = 2$!

Great job! You’ve isolated the variable using subtraction (and a little division).

Step 6: Check Your Answer

Always check your answer to make sure it fits back into the original equation.

If we put $x = 2$ back into the original equation $3x + 4 = 10$, we get:

$$3(2) + 4 = 6 + 4 = 10$$

That’s correct! Your answer works, meaning you did a great job isolating the variable.

Quick Recap

Here are the steps for isolating variables in linear equations with subtraction:

1. Know the structure of the equation.
2. Find the constant you need to remove.
3. Subtract that constant from both sides.
4. Simplify the equation afterward.
5. Isolate the variable with the right operations.
6. Check your answer by plugging it back in.

With practice, these steps will become easier. Soon, isolating variables will feel like a breeze. Happy solving!