2 1 Solving One Step Equations Equivalent Equations

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 +3 +3 x = 5 Check: ( ) - 3 = 2 (5)- 3 = 2 2 =2 Notice that we use the inverse of subtraction which Is addition to isolate the variable x.

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 Check: ( ) + 3 = 2 -3 -3 (-1)+ 3 = 2 x = -1 2 =2 Notice that we use the inverse of addition which Is subtraction to isolate the variable x.

We can use this procedure no matter where the variable is places, left or right of the equal sign: Ex: Solve ½ = + 3/2 4/2 = Check: ½ ½ = = y – 3/2 + 3/2 y y ( ) – 3/2 ( 2) – 3/2 (4/2) – 3/2 ½ 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 m = 84 Notice that we use the inverse of division which Is multiplication to isolate the variable m.

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

Solve:

Don’t forget to check your answer!!!

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-andinequalities/equations_beginner/e/one_step_equ ations

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