When solving two-step linear equations, many students make some common mistakes that can cause confusion and lead to wrong answers. Let's look at these mistakes and how to avoid them!

1. Forgetting the Order of Operations

One big mistake is when students forget to use the order of operations. This is especially important when you're adding or subtracting and also multiplying or dividing.

For example, think about this equation:

$3x + 5 = 20$

A lot of students jump right to isolating $x$ without first subtracting $5$ from both sides.

Here’s the right way to do it:

First, subtract $5$:

$3x = 20 - 5$
$3x = 15$

Then, divide by $3$:

$x = 5$

2. Forgetting to Do the Same Operation on Both Sides

Another common mistake is forgetting that whatever you do to one side of the equation, you have to do to the other side too.

Take this equation:

$2x - 4 = 10$

If a student adds $4$ to just one side, they might incorrectly write:

$2x = 14$

But the proper way to write it is:

$2x - 4 + 4 = 10 + 4$
$2x = 14$

3. Mixing Up Negative Signs

Negative signs can be tricky! For an equation like this:

$-2x + 6 = 0$

Some students accidentally drop the negative sign, which can lead to a wrong answer. It’s super important to remember that if you subtract (6), you get:

$-2x = -6$

Then, if you divide by $-2$, you get:

$x = 3$

Conclusion

Being aware of these common mistakes—like forgetting the order of operations, making sure to do the same thing on both sides, and handling negative signs correctly—can help students solve two-step linear equations more confidently and accurately.

Remember, practice makes perfect! The more problems you work on, the better you will get!