Variables in Addition and Subtraction Equations

When you were learning addition and subtraction, you encountered, or saw, a lot of problems like this:

In the last lesson, you learned that variables can take the place of numbers you don't know yet.ย

So let's re-write these problems using variables.

๐ We could replace each box by a letter.

Solving for the **value of the variable **is similar to finding what number goes into the box.

๐ All you need to do is "**undo" **whatever has been done with the variable.

Let's look at what that means with an example.

x + 6 = 9

What's been done with the variable x? ๐ค

That's right!

๐ 6 was added to the variable x.

How could we undo this?

That's right!

๐ We have to subtract 6.

**Tip: **Addition is the opposite of subtraction. To undo addition, you must subtract.

๐คBut how can we keep the **equation balanced **if we subtract 6 on the left side of the equation?

Correct!

To keep the **equation balanced**, whatever we do on one side, we must also do on the other side.

So if we subtract 6 from the left, we have to subtract 6 from the right side too.

Let's go ahead and solve it.

**x + 6 = 9**

**x + 6 - 6 = 9 - 6**

**x = 3**

We can add or subtract any number to one side of an equation, and as long as we do it to the other side too, the **equation remains balanced!**

Take a look:

๐ค Once we get something like "**variable = some number",** that is the value of the variable that makes the equation true!

The **value of the variable **that will make the **equation true **is called the **solution to the equation**.

That means the value of x is 3, and **x = 3** is the **solution to the equation**!

Let's try solving the second example.

10 - y = 2

What's been done to the variable y? ๐ค

๐ The variable y was subtracted from 10.

How can you undo this?

๐ Since y was subtracted from 10, let's try adding y and see what happens.

Just remember to do the same thing on both sides.

10 - y** + y = **2** + y**

**10 = 2 + y**

**Tip:** -y + y = 0, because anything minus itself equals 0.

Now we have an easier problem.

So what's our goal?

๐ Our goal is to get the variable **y alone **on one side of the equation. That's how we **solve the equation.**

So let's try subtracting 2 from both sides to get y alone:

10 = 2 + y

10 **- 2 **= 2 + y **- 2**

10 - 2 = 2 **- 2 + y**

8 = y

That means the value of y is 8, and **y = 8** is the **solution to the equation**!

To **solve an equation **with one variable, get the variable alone on one side of the equation and simplify the rest.

Let's look at one last example.

Solve for z:15 + 5 = z - 3

What has been done to the variable z?

๐ 3 was subtracted from the variable z.

How do you undo this?

๐ By adding 3 on both sides of the equation to keep it balanced.

**15 + 5 + 3 = z - 3 + 3**

**23 = z**

That means the value of z is 23, and **z = 23 **is the **solution to the equation**!

To check if your answer is right, replace the variable in the original equation by the number you found.

Checking, we have;

**15 + 5 = z - 3**

**15 + 5 = 23 - 3**

20 = 20

Since the left side is equal to the right side, that means we found the correct value of z.

Great! Now you know how to solve for the variable in an addition or subtraction equation. ๐

Are you ready for some practice? ๐ช

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