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Solving Algebra Equations
with Addition and Subtraction

The Equation

One of the basic concepts of algebra is the equation. The main thing to know about an equation is that everything on one side of the equal sign (=) must equal everything on the other side of the equal sign.


Variables are things that can change or have different values. In algebra, we are usually trying to find the value of one or more variables. In algebraic equations, the variable is represented by a letter.

On this page our variables will be represented by the letters "x" and "y".

Simple Equation

Here is a simple equation with x as the variable:

x + 5 = 7

What does x = ?

x = 2 because 2 + 5 = 7.

Solving an Equation

In the equation above we could just tell by looking at it that x = 2, however, this isn't always the case. Sometimes we have to work harder in order to solve for the equation.

We can sometimes solve an equation by adding or subtracting the same number to both sides of the equation. We know this is okay, because as long as we perform the same operation to both sides of the equation, then the equation doesn't change.

Let's try solving for this simple example by adding or subtracting to both sides:

x + 5 = 7

We want to find out what x equals, so we need to get x by itself on one side of the equation. If we subtract 5 from the left side, x will be by itself. Following our earlier rule, we need to do the same to right side.

(x + 5) - 5 = (7) - 5

x = 2

Another Example:

Solve for x:

x - 2y + 7 = y + 15

We need to get x by itself, so lets start by subtracting 7 from each side:

(x - 2y + 7) - 7 = (y + 15) - 7
x - 2y = y + 8

Now we need to get rid of the - 2y, we can do this by adding 2y to each side:

(x - 2y) + 2y = (y + 8) + 2y

x = 3y + 8

Now we should double check this answer by plugging it back into the original equation:

x - 2y + 7 = y + 15

Substitute 3y + 8 for x

3y + 8 - 2y + 7 = y + 15

3y - 2y + 8 + 7 = y + 15

y + 15 = y + 15

Here we have learned how to solve an equation by adding and subtracting to each side, but what if we have something like 2x = 4? To solve for that equation, we need to multiply and divide from each side. Go here to learn how to solve algebraic equations using multiplication and division.

Things to Remember

More Algebra Subjects
Algebra glossary
Linear Equations - Introduction
Linear Equations - Slope Forms
Order of Operations
Ratios, Fractions, and Percentages
Solving Algebra Equations with Addition and Subtraction
Solving Algebra Equations with Multiplication and Division

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