How to Solve Two-Step Linear Equations

Solving two-step linear equations might seem tricky, but it’s easier if you break it down into simple steps. The main goal is to find the value of a letter called $x$. To do this, you need to get $x$ by itself on one side of the equation. Here’s a simple guide to help you through the process.

What Does a Two-Step Equation Look Like?

A two-step linear equation usually looks like this:

$ax + b = c$

Here, $a$, $b$, and $c$ are numbers, and our job is to find out what $x$ equals.

Step 1: Find the Operations

First, look for the operations that are affecting $x$. In these equations, there are usually two main operations:

1. Multiplication or division.
2. Addition or subtraction.

Knowing these will help you understand what to undo first.

Step 2: Undo Addition or Subtraction

Next, you want to get rid of the number that’s being added or subtracted (that’s $b$). Use the opposite operation to do this:

• If $b$ is positive, subtract it from both sides.
• If $b$ is negative, add its positive version to both sides.

For example, let’s look at this equation:

$3x + 4 = 10$

To isolate $x$, you would subtract $4$ from both sides:

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

This simplifies to:

$3x = 6$

Step 3: Undo Multiplication or Division

Now that you have $3x$ isolated, you need to address the number $3$ in front of $x$. Again, use the opposite operation:

• If it’s multiplied by $x$, divide both sides by that number.
• If it’s divided by $x$, multiply both sides by that number.

Continuing from our previous example:

$3x = 6$

Now, divide both sides by $3$:

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

This tells us:

$x = 2$

Step 4: Check Your Solution

It’s always good to check your work. Replace $x$ back into the original equation and see if both sides are equal.

For our solution of $x = 2$, let’s check:

$3(2) + 4 = 10$

Calculating the left side gives:

$6 + 4 = 10$

Since both sides match, our solution is correct!

Step 5: Practice with Different Equations

To really get the hang of this, practice with a few different equations. Here are some examples:

1. $5x - 3 = 22$
2. $4x + 1 = 25$
3. $-2x + 8 = 0$

Let’s solve them using the steps we learned:

1. For $5x - 3 = 22$:

   • Add $3$ to both sides: $5x = 25$
   • Then divide by $5$: $x = 5$

2. For $4x + 1 = 25$:

   • Subtract $1$: $4x = 24$
   • Divide by $4$: $x = 6$

3. For $-2x + 8 = 0$:

   • Subtract $8$: $-2x = -8$
   • Divide by $-2$: $x = 4$

Conclusion

Learning how to solve two-step linear equations is an important skill in math. It not only helps you in tests but also makes understanding other math topics easier. By following these clear steps, you can work through equations with confidence.

Here's a quick recap of what to do:

1. Identify and undo addition or subtraction.
2. Isolate the $x$ term by undoing multiplication or division.
3. Check your answer to make sure it’s correct.
4. Practice with different problems to improve your skills.

By sticking to these steps, you can tackle two-step linear equations easily and boost your math confidence.