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When two sides in a mathematical statement are equal, it is called an equation. To solve an equation, you must collect like terms and put the distributive law in to effect. Keep in mind the following integer rules
  • Two positives remain positive
  • Two negatives make a positive
  • A positive and a negative result in a negative
When solving an equation, you are trying to isolate the unknown variable. To do so, it is essential use opposite operations to collect like terms and simplify your equation. Remember, what you do on one side you must do to the other. For example, 3x + 5 = 11, 3x + 5 - 5 = 11 - 5, 3x / 3 = 6 / 3, x=2 This way, by subtracting the fives on the left side and dividing by three, all known terms and coefficients are cancelled, and by subtracting five and dividing by three on the right side, you solve for x. Therefore the unidentified variable must be on the opposite side from the known terms. When using opposite operations, you must be very careful that you use the proper operation.
Opposite Operations:
  • Division = Multiplication
  • Multiplication = Division
  • Addition = Subtraction
  • Subtraction = Addition


Examples-
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1. X + 4 = 13
X + 4 - 4 = 13 - 4 ---> Subtract 4 from each side to elimante the 4 on the left and still have the equation be true.
X = 9 ---> Collect like terms.

‍‍‍‍2. -V= 9
-V / -1 = 9 / -1 ---> When there is no coefficient beside a variable, you must always imagine a 1 infront of the variable, so when the variable is negative, the coefficient is also negative. Therefore, you must divide both sides be -1 to make the variable positive.
V = -9 ---> Collect like terms. Since the 9 was a positive then divided by -1, it becomes a -9.‍‍‍‍

3. A student council has raised $500 in a school spirit fundraising drive. The council decides to use the funds to buy school T-shirts to give away at a pep rally. If the T-shirts cost $6 each, how many can the student council buy?

n = number of T-shirts the student council can buy. ---> Choose a variable (letter) to represent the unidentified term.
6n = 500 ---> Write out the equation.
6n / 6 = 500 / 6 ----> Divide both sides by 6 to eliminate the coefficient and keep the equation true.
n = 83.3 ---> Collect like terms.

Practice-

1. Solve
a) x - 5 = 4 b) m + 8 = 11simple_equation_1.jpg
c) y - 3 = 0 d) h + 2 = 6

2. Solve.
a) 3x = 12 b) 5y = 20
c) n / 3 = 8 d) -2k = 16

3. Solve. Check you answers.
a) k - 4 = -9 b) 6x - -30
c) q / 7 = 2 d) 2y - 7 = 9
e) -3w - 1 = 14 f) 2q - 9 = -13

Apply-

4. At a bake sale, pies cost $7 each. One customer buys $84 worth of pies.
a) Write an equation to model the number of pies the customer bought.
b) Solve the equation.

5. Justine's mother is building an ultralight airplane. The fuel tank is made of plastic and has a mass of 5000 g. Each litre of gasoline has a mass of 840 g. The total mass of the plane plus the tank cannot exceed 21 800 g.
a) Write an equation that models the number of litres of gasoline that the tank may hold.
b) Solve the equation to determine the number of litres of fuel in a full tank.

Practice Test-

Ready for the test? Complete the following practice tests to find out! Good Luck!!

http://www.proprofs.com/quiz-school/story.php?title=Solving-One-Step-Equations-Containing-Integers-1
http://www.bbc.co.uk/scotland/learning/bitesize/standard/maths_ii/algebra/quiz/solving_simple_equations/
http://www.mytestbook.com/test_questions.aspx?topics=Algebra%20Simple%20Equations%20Algebraic%20Reasoning&subject=Math&grade=4&test_id=289

Games-

Do you like computer games? Are you too busy studying math to play any? Well now, you can learn AND have fun!!!
Try these very fun and addicting but educational math games:

http://www.math-play.com/One-Step-Equation-Game.html
http://www.math-play.com/soccer-math-one-step-equations-game/one-step-equations-game.html
http://math4children.com/Grade2/games/Balancing_equation_en_garde%20game/index.html <---I recommend this one!!!

Don't Forget....


If you ever need help remembering how to solve simple equations, try to remember these catchy videos: