Solve Equations with Addition

A crucial beginning step of algebra is being able to solve equations with addition or subtraction.  This lesson is designed with the beginning algebra student in mind.  We will take you from the very beginning.


Examples for Solving Equations

Example #1:  Solve x + 4 = 9

To solve, we must identify our variable:  x.  Then we have to look at the other terms on the same side of the equation:  + 4.  Then, we must do the opposite (-4) from both sides of the equations.

x + 4 = 9 original equation
– 4 = – 4 subtract 4 from both sides
x = 5 simplify both sides (answer)


As you can see, the answer to the first example is 5. If you think back to the original problem, it is saying "what number plus 4 equals 9?" Well, we know that 5 plus 4 equals 9. Now you might be thinking that you don't have to go through all those steps - you just know it is equal to 5, but trust us, you will want to know the steps for when the problems get more challengins.

Let's look at another example:


Example #2:  Solve x – 3 = 8

In this equation, we must add 3 to both sides...

x 3 = 8 original equation
+ 3 = + 3 add 3 to both sides
x = 11 simplify both sides (answer)

Again, looking back at the original problem, "what number minus 3 equals 8?" We know 11 minus 3 equals 8!

Example #3:  Solve x  = 9 + 5

To solve equations using addition, sometimes all you really need is addition!  In this case, we can simply add the right hand side

x = 9 + 5 original equation
x = 14 simplify the right hand side (answer)

This problem is easy - 9 plus 5 equals 14!

Congratulations, you know now how to solve equations with addition! Next you might want to learn how to solve equations with division. These types of problems are similar, so you should catch on pretty quickly.

If you had a little trouble wtih this page, don't worry - our fundamental skills for how to solve linear equations can help! Good luck!




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