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# Solving Linear Equations

An equation has two expressions, separated by an equal sign:**(expression)** = **(expression)**

In any operation, the two expressions will remain equal.

To solve an equation we can:

- Add the same quantity to both sides

- Subtract the same quantity from both sides

- Multiply both sides by the same number

- Divide both sides by the same number

For example, let’s take the simple example 2 + 2 = **4**.

If we add 6 to both sides with get 4 + 2 + 2 = **4 + 4**. The answer is 8.

Now, you don’t usually work with equations where all the numbers are known, but rather where one is unknown. We call this a variable. Your job is to solve the variable to make the equation equal on both sides.

Often the variable is given a letter: x = something.

Let’s solve the equation: x – 2 = **3**

We can write this equation as x + (-2) = **3**

Adding two positives to both sides will cancel the two negatives on the left hand side:

x + (-2) + 2 = **3 + 2**

The two positives and the two negatives cancel each other out: (-2) + 2 is 0.

So **x = 5**.

Let’s try this example: 3x – 6 = **9**.

Add 6 to both sides: 3x – 6 + 6 = **9 + 6**

The six negatives and the six positives cancel each other out on the left-hand side, so:

3x = **9 + 6**

Now we want to find out what x is.

Divide by 3 on both sides to work out what x is:

3x / 3 = **15 / 3**

The answer is **x = 5**.

For more practice, we sell a workbook on linear equations in our bookstore.