# Equations

The sign = means, is equal to. In other words, there is exactly the same amount on both sides of the = sign.

For example, *3 + 7 = 10*. There are ten on each side of the equation because* 3 + 7* is ten. The solution to an equation is based on that same consideration. Both sides must have exactly the same amount.

*4 + _ = 9*

Which number fits the blank space? Many find the missing number to be five. Because 4 + 5 = 9. It is equal on both sides.

But guessing is not a very good way to solve an equation, so we need the right tools for it. We can modify the equation as long as we remember that, whatever we do, we must do it on both sides of the equation. See examples 1 and 2.

Video lesson about solving equations. Turn on the subtitles if needed

Also, we note that addition cancels subtraction and multiplying cancels division. In other words, if we count two plus one, we get three. To get back to beginning, we subtract one from three.

If we multiply a number by another number, we can revert back by dividing by the same number.

**Example 3.**

Solve the equation* 3x + 2 = 8*

*3x + 2 = 8 || -2*

*3x + 2-2 = 8-2*

*3x = 6 ||: 3*

*x = 6/3*

*x = 2*

So the goal is to eliminate all the numbers around *x* so that only *x* is left.

**Example 4**

Find the constant a so that the solutions for the equation is *2.*

This means that *x = 2*. We replace x by number *2* and find *a*.

When *a = -6, x = 2*

**Turn on the subtitles if needed**