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∙

Ex: Solve = 12

Notice that we use the inverse of division which Is multiplication to isolate the variable m.

m = 84

Check: = 12 = 12

= 12 12 = 12

(7) = 12(7)

Division Property: for any real numbers a, b, and c,

if a = b, then =

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:

Thus: 36 = t

The fraction is multiplying t thus the opposite is division. However, we never divide fractions. We always use the inverse of the given fraction.

36 = t

= t t =

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

x=−𝟑𝟔

VIDEOS: One StepEquations

One Step:

http://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/equations_beginner/e/one_step_equations

Class Work:

Pages: 85 – 87

Problems: As many as you need to master

the concepts.