How to solve equations

How to solve equations

1-2 step equations

The Foundation

• the goal is to isolate the variable to one side of the equal sign with a coefficient of 1 (Ex: x = 3)

• Undo everything that was done to the variable in reverse order- start with what was done last

• What you do to one side of the equation, you MUST do to the other side also (Ex: if I add 3 to the left side, I must add 3 to the right side too)

Example

5x + 3 = 18

1. Read starting with the variable first: x multiply 5 add 3 equals 18

Multiple Choice

What was done last to the variable? 5x + 3 = 18

• add 3

• multiply 5

Multiple Choice

How do we undo add 3?

• multiply 3

• divide 3

• add 3

• subtract 3

Multiple Choice

how do we convert subtract 3 to addition?

• add -3

• add 3

Let's do it!

Bring down the 5x.

What is 3 + (-3)?

What is 18 + (-3)?

Multiple Choice

What is 3 + (-3)

• 6

• -6

• 0

• 1

Multiple Choice

What is 18 + (-3)

• 15

• -15

• 21

• -21

Step 2

What was done before add 3 and how do we undo it

x multiply 5 add 3 equals 18?

Multiple Choice

What was done before add 3 and how do we undo it

x multiply 5 add 3 equals 18?

• multiply 5; divide 5

• add 3; subtract 3

• multiply 5; add 5

• mulitply 5; subtract 5

Divide by 5 on both sides and simplify

x = 3

Let's try another!

Before we can determine what was done last, we need to perform the distributive property!

Before we start....

• change the subtraction to addition: -6x - 3

• then we can perform the distributive property

Multiple Choice

-6x - 3 coverted to addition becomes

• -6x + 3

• -6x + (-3)

• 6x + 3

Distributive Property

1. -4 * (-6x) = 24x and

2. -4 * (-3) = 12

Now we can use 24x + 12 = 12 to determine what was done last to our variable

Multiple Choice

How is this equation read 24x + 12 = 12, starting with the variable?

• x divide 24 add 12 equals 12

• x multiply 24 add 12 equals 12

• x subtract 24 add 12 equals 12

Multiple Choice

What do we do first?

x multiply 24 add 12 equals 12

• subtract 12 from both sides

• divide 24 on both sides

• multiply 12 on both sides

• add 12 on both sides

Multiple Choice

What do we do next? x multiply 24 equals 0

• divide 24 on both sides

• multiply 24 on both sides

• add 24 on both sides

• subtract 24 from both sides

Multiple Choice

What is x?

• x = 0

• x = 24

• x is unknown

• who is x

Poll

How do you feel about solving equations so far?

• great

• ok

• still have some questions

• mostly lost

• HELP!!!!