Introduction to Equations Lesson 2.1.7/2.1.8 (Alternate)

Prior like terms

Prior

Today… You are going to utilize those skills to help you solve equations.

Let’s Get Started… Section 1:Introduction to Equations Section 2:Review of Equations with One Operation. Section 3:Equations with Two Operations. Section 4:Combining Like Terms

What is an Equation?

multiply

Here is the dilemma …

Goal However, you can’t just erase them. That would not be a “legal” move”!

Goal

O Before we look at exactly how to get a variable by itself, I wanted to show you a couple of pictures that I think will help you understand one of the new concepts that we will learn later on in the lesson. O I have a couple of pictures of some Weightlifters.

Weightlifters I’m not sure who this athlete is, but previous students gave him a name. He got his first name, “Harry”, from HLMS. Then, SMS students gave him his last name…. Harry Pitts And yes… there are female Olympic weightlifters too. This is… Zoe Smith from the UK

O Notice in the picture that on each side of the barbell, there is the exact same number of weights. O Can anyone take a guess as to what would happen if the weightlifters took a weight off one side, but not the other side… then tried to lift the barbell?

O Would it be safe to say… if Harry adds weight to one side of the barbell, then Harry must add the exact same amount of weight to the other side of the barbell… So that it is balanced ? YES

O Would it be safe to say… if Zoe takes away weight from one side of the barbell, then Zoe must take away the exact same amount of weight from the other side of the barbell… So that it is balanced ? YES

O What ever you do to one side of an equation, you must ALWAYS do to the other side. GOAL

Steps to Solving any Equation The first 2 steps are not always necessary. This is where you are going to work on getting that variable by itself. We use inverse operations to do the “undoing”. Step 1 Distribute to get rid of any parentheses. Step 2 Combine any like terms. Step 3 Solve the simplified equation by “undoing”. Step 4 Check your solution.

Inverse Operations Subtraction (-) Addition (+) Multiplication () Division ( ÷)

Moving On… Section 1:Introduction to Equations Section 2:Review of Equations with One Operation. Section 3:Equations with Two Operations. Section 4:Combining Like Terms

Let’s look at some simple equations first… Watch how we use the inverse operations to get the variable alone.

O Click to Watch Demo Check Solution Step 1 Distribute to get rid of any parentheses. Step 2 Combine any like terms. Step 3 Solve the simplified equation by “undoing”. Step 4 Check your solution.

Check Solution Step 1 Distribute to get rid of any parentheses. Step 2 Combine any like terms. Step 3 Solve the simplified equation by “undoing”. Step 4 Check your solution. Guided Practice # 1

Check Solution Step 1 Distribute to get rid of any parentheses. Step 2 Combine any like terms. Step 3 Solve the simplified equation by “undoing”. Step 4 Check your solution. Guided Practice # 2

You Try Check your solutions !

Let’s look at a couple of equations that deal with either multiplication or division… Again, your goal is to get the variable alone.

Check Solution Step 1 Distribute to get rid of any parentheses. Step 2 Combine any like terms. Step 3 Solve the simplified equation by “undoing”. Step 4 Check your solution. O Click to Watch Demo

Check Solution Step 1 Distribute to get rid of any parentheses. Step 2 Combine any like terms. Step 3 Solve the simplified equation by “undoing”. Step 4 Check your solution. O Click to Watch Demo =

Check Solution Step 1 Distribute to get rid of any parentheses. Step 2 Combine any like terms. Step 3 Solve the simplified equation by “undoing”. Step 4 Check your solution. Guided Practice #3

Check Solution Step 1 Distribute to get rid of any parentheses. Step 2 Combine any like terms. Step 3 Solve the simplified equation by “undoing”. Step 4 Check your solution. Guided Practice #4

Check Solution Step 1 Distribute to get rid of any parentheses. Step 2 Combine any like terms. Step 3 Solve the simplified equation by “undoing”. Step 4 Check your solution. Guided Practice #5

You Try Check your solutions !

Moving On… Section 1:Introduction to Equations Section 2:Review of Equations with One Operation. Section 3:Equations with Two Operations. Section 4:Combining Like Terms

O When an equation involves more than one operation, you “undo” in reverse. In reverse of what? …of order of operations.

Then, get rid of this. What does that mean? O Looking at the below equation, we have multiplication (4x) and subtraction (- 7). O Order of operations requires multiplication to be done before subtraction… PEMDAS O However, when solving an equation, you undo in the reverse order. You have to undo the subtraction first, then the multiplication. Get rid of the subtraction first!

Check Solution Step 1 Distribute to get rid of any parentheses. Step 2 Combine any like terms. Step 3 Solve the simplified equation by “undoing”. Step 4 Check your solution. O Click to Watch Demo

Guided Practice #6 Check Solution Step 1 Distribute to get rid of any parentheses. Step 2 Combine any like terms. Step 3 Solve the simplified equation by “undoing”. Step 4 Check your solution.

Guided Practice #7 Check Solution Step 1 Distribute to get rid of any parentheses. Step 2 Combine any like terms. Step 3 Solve the simplified equation by “undoing”. Step 4 Check your solution.

Guided Practice #8 Check Solution Step 1 Distribute to get rid of any parentheses. Step 2 Combine any like terms. Step 3 Solve the simplified equation by “undoing”. Step 4 Check your solution.

You Try Check your solutions !

Last Section… Section 1:Introduction to Equations Section 2:Review of Equations with One Operation. Section 3:Equations with Two Operations. Section 4:Combining Like Terms

Step 1 Distribute to get rid of any parentheses. Step 2 Combine any like terms. Step 3 Solve the simplified equation by “undoing”. Step 4 Check your solution. O Click to Watch Demo

Guided Practice #9 Check Solution Step 1 Distribute to get rid of any parentheses. Step 2 Combine any like terms. Step 3 Solve the simplified equation by “undoing”. Step 4 Check your solution.

You Try Check your solutions !

Closure O What was the male weightlifter’s name? O What was the female weightlifter’s name? O What does weightlifting have to do with equations? O What is the Golden Rule of Algebra? O What are the 4 steps of solving any equation? O When solving an equation with multiplication and subtraction, which do you “undo” first? Why? O How do you check your solution after solving an equation?

Closure DON”T FORGET… Always balance or the result can be bad.