 # 2.1 Solving One Step Equations: Equivalent Equations: equations that have the same solutions. Isolate: Get a variable with a coefficient of 1 alone on.

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2.1 Solving One Step Equations: Equivalent Equations: equations that have the same solutions. Isolate: Get a variable with a coefficient of 1 alone on one side of the equation. Inverse Operations: Opposite operations that undo other operations.

GOAL:

We can find the solution to one step equations by using inverse operations: Addition Property: for any real numbers a, b, and c, if a = b, then a + c = b + c Ex: Solve x – 3 = 2 Notice that we use the inverse of subtraction which Is addition to isolate the variable x. + 3 + 3 x = 5 Check: ( ) - 3 = 2 (5)- 3 = 2 2 = 2

We can find the solution to one step equations by using inverse operations: Subtraction Property: for any real numbers a, b, and c, if a = b, then a - c = b - c Ex: Solve x + 3 = 2 Notice that we use the inverse of addition which Is subtraction to isolate the variable x. - 3 - 3 x = - 1 Check: ( ) + 3 = 2 (-1)+ 3 = 2 2 = 2

We can use this procedure no matter where the variable is places, left or right of the equal sign: Ex: Solve ½ = y – 3/2 + 3/2 + 3/2 4/2 = y Check: ½ = ( ) – 3/2 ½ = ( 2) – 3/2 ½ = (4/2) – 3/2 ½ = ½ 2 = y Remember that when you add or subtract fractions we must find a common denominator!!

Multiplication Property: for any real numbers a, b, and c, if a = b, then a ∙ c = b ∙ c Notice that we use the inverse of division which Is multiplication to isolate the variable m. m = 84

Ex: Solve 4z= 12 Notice that we use the inverse of multiplication which is division to isolate the variable m. z = 3 Check: 4z = 12 4( ) = 12 4(3) = 12 12 = 12 __ __ 4 4

Solve:

Check: Thus we have the correct answer.

YOU TRY IT: What is the solution to

SOLUTION: inverse of division

VIDEOS: One Step Equations One Step: http://www.khanacademy.org/math/algebra/solvi ng-linear-equations-and- inequalities/equations_beginner/e/one_step_equ ations

Class Work: Pages: 85 – 87 Problems: As many as you need to master the concepts.

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