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Quick introduction to Algebra 1


Manipulating Expressions

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

Description

In this tutorial we will cover Algebra 1 with examples. This is really a quick introduction to Algebra 1. This tutorial will suit students who want to check out what Algebra is all about or for students who wants to quickly brush up their Algebra knowledge

Topics for this tutorial includes

  1. Quick background on Algebra
  2. Variables and expressions
  3. Algebraic multiplication
  4. Expressions
  5. Order of operations
  6. Algebra basic definitions
  7. Commutative, Associative and Distributive Laws
  8. Manipulating Expressions
  9. Writing and interpreting expressions.
  10. Expressions adding fractions
  11. What next

This quiz is followed up with a BODMAS based quiz, which is absolutely free to take and test your knowledge.

I hope that you will enjoy this tutorial. Please leave your feedback and improvement suggestions



Prerequisites

Mathematics knowledge including pre algrebra, multiplication, subtraction, additions etc is essential

Audience

Students starting with Algebra 1 or students looking to quickly brush up their Algebra 1 knowledge.

Learning Objectives

Learn Algebra 1

Author: Subject Coach
Added on: 27th Jan 2015

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