Warm up Lesson 2.2 Use the distributive property to simplify each expression:

Warm up Answers

Lesson 2.2 Solving One and Two Step Equations Strand 1 Concept 2 P.O. 2 Obj: SWBAT Summarize the properties of and connections between real number operations; justify manipulations of expressions using the properties of real number operations.

Let’s Review…. What is an equation? An equation is a mathematical statement that two expressions are equal. This means, it has an equals sign in it!

Solving Basic Equations When solving equations, your mission is to get the variable by itself! It may start out looking messy, but by the end it should look something like this: x = 3, or a = 42, or -16 = m

Inverse Operations… The most important tool you will learn today and use when solving equations is inverse operations. Another word for inverse is opposite! An inverse operation It is an operation that undoes a previous operation. Consider the basic mathematical operations: addition, subtraction, multiplication, and division. Each one of these has an inverse…let’s make a table:

Inverse Operations Table… OperationInverse Operation Addition Subtraction Multiplication Division Subtraction Addition Division Multiplication

What does this all mean? What this means for us now, is that when a number is being added to a variable, to get rid of it, we must subtract it. Or if a number is being multiplied by a variable, we have to divide. Keep in mind that the equals sign tells us that whatever we do to one side, we must do to the other!

We refer to these inverse operations using special properties: The addition property of equality The subtraction property of equality The multiplication property of equality The division property of equality Special Property Names:

Practice… Solve the following for the indicated variable: a = -3 y = 28 x = -11 m = -35

More Decimals Practice… a = y = x = 14.6 m =

What is a reciprocal? A reciprocal is a multiplicative inverse which is just a fancy way of saying take a fraction, flip its top and bottom, and multiply by that new value! Given: Its reciprocal is:

And still there is more… Solve the following for the indicated variable: a = 43/8 or 5 3/8 y = 29/28 or 1 1/28 x = 40/33 or 1 7/33 m = -14/3 or -4 2/3

Solving 2-step equations How do we solve problems such as Step 1: Isolate the variable by using the addition or subtraction property of equality. -15 Step 2: Combine Like Terms (Simplify) Step 3: Isolate the variable using the multiplication or division property of equality and simplify 33

Let’s check to make sure we did our work correctly Start with the original problem Substitute the variable with the answer you came up with remember to put your answer in ( ) (10) Next, Simplify = = 45 When you have the reflexive property (a true statement such as this, you should have done all your work correctly

Let’s try another one -15 Let’s see if we did this right: remember start with the original problem, then use the order of operations to simplify both sides of the equal sign = = 25

What happens when… we have a problem like Step 2: Isolate the variable use the subtraction property of equality -15 Step 3: Combine Like Terms (simplify) Step 4: Isolate the numerator by using the division property of equality Don’t forget to check Step 1: simplify -5

Now, You try some on your own be sure to check your work!

Summary Explain why inverse operations are used when solving an equation. Homework: Worksheet 2.1