Algebra Tutorial: Equations with Variables

Equations with Variables

So far we've only considered equations with numbers and no variables (letters).

In algebra, we often see equations that contain a variable like x. Here is an example:

x+1=6

Suppose we wanted to solve this equation:

x+1=6

To solve this equation, we need to find a number that we can plug in for x to make the equation true.

If we plug in x=5, we see that after we replace x with 5, the equation

x+1=6

becomes

5+1=6

which is true.

Thus the solution to the equation x+1=6 is:

x=5

(In Algebra Calculator, we can use the "@" command to plug in the solution x=5 into the equation x+1=6: x+1=6 @ x=5)

Consider again the equation:

x+1=6

Let's show that x=4 is not a solution.

If we replace x with 4, the equation

x+1=6

becomes

4+1=6

which is false.

(You can see this substitution happen in Algebra Calculator: x+1=6 @ x=4)

Thus, x=4 is not a solution for x+1=6.

x=5 is the only solution that works.