Understanding Linear Equations Made Simple

When working with linear equations that involve addition, it's important for 11th graders to find ways to get the variable alone.

Let’s look at some easy steps that can help!

What is a Linear Equation?

First, let’s know what a linear equation is. A simple example of one is:

$$x + 5 = 12$$

Our main goal is to get $x$ by itself on one side of the equation. This is called isolating the variable.

Easy Steps to Follow

1. Find the Constant: First, spot the number that is added to your variable. In our example, the constant is $5$.

2. Subtract to Get the Variable Alone: To get $x$ by itself, we can subtract $5$ from both sides. Here’s how:

   $$x + 5 - 5 = 12 - 5$$

   Now, we simplify this to:

   $$x = 7$$

   Great! Now $x$ is alone!

3. Check Your Answer: It’s always a good idea to make sure your answer is right. If we put $7$ back into the original equation:

   $$7 + 5 = 12$$

   This is correct, so our answer works!

Let’s Try Another Example

Now, let’s practice with another equation:

$$2y + 3 = 11$$

1. Find the Constant: This time, the constant is $3$.

2. Subtract to Isolate the Variable: We can subtract $3$ from both sides:

   $$2y + 3 - 3 = 11 - 3$$

   This simplifies to:

   $$2y = 8$$

3. Divide to Finalize: To get $y$ all by itself, divide both sides by $2$:

   $$y = \frac{8}{2} = 4$$

Wrapping Up

Always remember, isolating the variable with addition and subtraction means doing the opposite actions. Whatever you do to one side of the equation, make sure to do the same to the other side.

With practice, these steps will make isolating variables easy!