The Keys to Learning Basic Algebra

Convinced that learning basic algebra is far from basic?  These 3 key algebraic concepts will make life a lot easier.

1. Expressions vs Equations--What is the Difference?

Up until the time you reached algebra, the equal sign, =, was probably used as a way of signifying the answer to a problem.  Now that we are growing into higher levels of math, the equal sign will now be used as a way of separating the two sides of an equation.

The easiest way to determine if you have an expression or an equation is by asking yourself this question:  "Does my problem have an equal sign in it?"  If the answer to this question is yes, then you have an equation.  Look, the word equation has the first four letters of the word equal right in it.  *Remember, equations have equal signs, expression don't.*



Equations (equal sign)

Expressions (no equal sign)

    2x = 12 3x + 4
    y = 4x - 2 5x + 2y
    3x + 5y = 15 8x + 3y + 6


2. Simplify Expressions by Combining Like Terms

Expressions need simplified - we do this by combining like terms.  A "like term" is a number that has the same letter attached to it.


To give expressions more meaning, you can give each letter a name.

     Let x stand for x-box (or x-ray, whatever you want...)


Looking back at the first expression above, it should make sense to you that "3 x-box's plus 2 x-box's makes 5 x-box's."

Another Example: 

3x + 4y

Is NOT 7x or 7y  - leave it as 3x + 4y


Let x stand for x-box and y stand for yoohoo

Remember, 3 x-box's and 4 yoohoo's cannot combine!  In terms of math, leave the expression 3x + 4y as it is - you cannot simplify it.

One More Example:


2x + 3

Each letter is its own group, and can only be combined with other numbers with the same letter.  The plain numbers (2, 5, 13, -8, etc.) are a separate group as well.  You can think of these as dollar bills.

2 x-box's and $3 cannot combine.  Leave 2x + 3 as it is.

* Helpful tip give each lettered group a different color - then combine only numbers that have the same color.  Take a look...

4x + 2y + 5x + 3 + 9y + 10         (original expression)

9x + 11y + 13                  (simplified expression)      

* Do not combine the different colors

Do you get it?  Good, you are learning basic algebra! 

3. Solve Equations by Isolating the Variable

Equations have equal signs.  This means that your answer should also have an equal sign in it - like x = 4.  Being able to properly solve equations is essential to learning basic algebra.

The equal sign in an equation separates the two sides of the equation into the left hand side (LHS) and the right hand side (RHS).  Viewing the equal sign as a divider instead of an answer mark is essential to learning basic algebra. 

Example:  LHS


4x + 2x


10 + 8







Each side of the equation is actually an expression.  Simplify each expression first if it is possible.  Take a look back at the lesson on combining like terms if you are unsure. 

Once you have combined all like terms, it is time to solve for your variable.  You need to remove everything else by doing the opposite.  In the example above, I got rid of 6 times x, by dividing by 6.  

A more in depth look of how to solve equations is also available if you think you need more help with that key to learning basic algebra.

Hopefully these three key points will help make learning basic algebra easier for you.  You may want to explore some of our free printable math worksheets as a nice way to practice.





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