Using Algebra to Solve Equations

Lets review algebraic expressions A # increased by 5 A # decreased by 5 A # divided by 5 A # multiplied by 5 Formula for the area of a rectangle x + 5 x - 5 x 5 5 x lw

Solving Equations Algebraically

The only rules that you need to know... Rule #1 - ISOLATE the variable on one side of the equation Rule #2 - whatever you do to one side, you do the EXACT same thing to the other

3x + 10 = 19 Equation in words: 3 times a # increased by 10 is 19 X = 3

Isolate the Variable on one side of the equation Math Rule #2 - whatever you do to one side, you do the EXACT same thing to the other 3x + 10 = 19 Isolate the variable means that only the x is on the left side 3x + 10 = 19 3x = 9 3 3 X = 3 -10 -10

Isolate the Variable on one side of the equation Math Rule #2 - whatever you do to one side, you do the EXACT same thing to the other 5n - 2 = 348 5n - 2 = 348 5n = 350 5 5 n = 70 +2 +2

Isolate the Variable on one side of the equation Math Rule #2 - whatever you do to one side, you do the EXACT same thing to the other 2n +3 = 4 2n +3 = 4 2n = 1 2 2 N = 1/2 -3 - 3

1. 7x - 7 = 42 2. 5x + 9 = 19 3. 5y + 8 = 9 4. 56x - 78 = -22 5. 50x + 50 = 150 Isolate the Variable on one side of the equation Math Rule #2 - whatever you do to one side, you do the EXACT same thing to the other

1. 7x - 7 = 42 2. 5x + 9 = 19 3. 5y + 8 = 9 4. 56x - 78 = -22 5. 50x + 50 = 150 x = 7 x = 2 y = 1/5 x = 1

Expanding 4(5+n) = 20 + 4n a(b+c) = ab + ac Same as (a x b) + (a x c) Expanded form 4(5+n) = 20 + 4n

State the following in expanded form a) 5(x + 6) b) 7(5 + e) = 5x + 30 = 35 + 7e a(b+c) = ab + ac Same as (a x b) + (a x c)

One Last Important Concept: Combining Like Terms

As long as the variable is EXACTLY the same letter, they can be combined If the variables are the same, they are referred to as LIKE TERMS 6x + 4x = 3n + n = 5n - n = 14a - 10a = 10x 4n 4n 4a

14t - 4s -3x 12j - 4r 10n - 4n2 7x - 10x = 5j + 7j - 4r = When we combine like terms, it is also referred to as simplifying Simplify the following expressions: 4t + 10t = 6s - 10s = 7x - 10x = 5j + 7j - 4r = 3n – 4n2 + 7n = 14t - 4s -3x 12j - 4r 10n - 4n2

Steps to solving algebraic equations: Simplify (combine like terms) 4x + 6x = 100 10x = 100 10 10 x = 10 To double check our answer, substitute (10) into the original question: 4(10)+ 6(10) = 40 + 60 = 100 Steps to solving algebraic equations: Simplify (combine like terms) Isolate the Variable on one side of the equation Math Rule #2 - whatever you do to one side, you do the EXACT same thing to the other

Steps to solving algebraic equations: Simplify (combine like terms) 4x - 12 = 3x 4x -12 = 3x x - 12 = 0 x = +12 To double check our answer, substitute () into the original question (left side and right side): Left Side (LS): Right Side (RS): 4x - 12 3x = 4(12) - 12 = 3(12) = 48 - 12 = 36 = 36 -3x -3x Steps to solving algebraic equations: Simplify (combine like terms) Isolate the Variable on one side of the equation Math Rule #2 - whatever you do to one side, you do the EXACT same thing to the other +12 + 12

Steps to solving algebraic equations: Simplify (combine like terms) 5x – 40 = 3x 5x -40 = 3x 2x - 40 = 2x = 40 2 2 x = 20 Double check our answer LS: RS: 5x - 40 3x = 5(20) - 40 = 3(20) = 100 - 40 = 60 = 60 -3x -3x Steps to solving algebraic equations: Simplify (combine like terms) Isolate the Variable on one side of the equation Math Rule #2 - whatever you do to one side, you do the EXACT same thing to the other +40 + 40

-20 = -4x - 6x Why is this a tricky question? Subtract integers Combining like terms Isolate the variable