Quick introduction to Algebra 1

Combining like terms

In simple addition we add all the numbers together to get the sum. In algebra, sometimes numbers are attached to variables and we need to make sure that the variables are alike before we add them. Two different variables such as X and Y are considered unlike terms.

Eg 1: 6x + 11 - x - 6 + 2x

Simplify the above equation by combining the like terms, all the numbers with the term x in them are like terms (6x, x, and 2x are like terms). All numbers without x are like terms (11 and 6 are like terms). To solve this equation, we rewrite the problem with the x terms together and the numbers together

6x – x + 2x + 11 – 6

Now it’s pretty easy, add or subtract all the x terms first

6x – x + 2x = 7x

Now rewrite the equation

7x + 11 -6

Now add/subtract the regular numbers

11-6 = 5

The equation is

7x + 5

Eg 2: Solve x + 8 + 7x + 1 =73

First combine the like terms

x+ 7x + 8+1 =73

8x + 9 =73

Subtract 9 from both sides

8x +9 -9 = 73-9

8x = 64

Divide by 8 on both sides

8x /8 =64/8

x= 8

Eg 3: 3x - 6 -9y + 12x +y

Combine the like terms

3x + 12x -9y+y -6

15x -8y -6 cant simplify any further.

Eg 4: a little complicated expression to simplify

-4y +4x -3xy + 2xy + x2 + 3y2 -5x2 -2y2-4xy + y -2x

Combine the like terms first,

-4y + y +4x -2x -3xy + 2xy - 4xy + x2 -5x2 + 3y2-2y2

= -3y +2x -5xy-4x2+y2

Adding two expressions

We can also, add two expressions.

To add the expression 3x +2 and -2/3 –x

3x + 2 -2/3 – x

Add the x terms

2x + 2 - 2/3

Now simplify the constants

(2 x 3)/3 – 2/3 = 6/3 -2/3

(6-2)/3 = 4/3

So the answer is 2x +4/3