chapter 3 solving linear equations. throughout mathematics, you encounter many types of equations

Chapter 3Solving Linear Equations

Throughout mathematics, you encounter many types of equations.

Throughout mathematics, you encounter many types of equations.

• some with only 1 variable (one unknown value)

Throughout mathematics, you encounter many types of equations.

• some with only 1 variable (one unknown value)

AND

x 3 10 ( )x 7 9 4 108

Throughout mathematics, you encounter many types of equations.

• some with only 1 variable (one unknown value)

AND

• some with 2 variables

x 3 10 ( )x 7 9 4 108

Throughout mathematics, you encounter many types of equations.

• some with only 1 variable (one unknown value)

AND

• some with 2 variables

… and guess what?

x 3 10 ( )x 7 9 4 108x y 12 9 15

some have MANY variables, and exponents, and radicals, and lots of other “cool” stuff…

some have MANY variables, and exponents, and radicals, and lots of other “cool” stuff…

xy

x

22164 36

some have MANY variables, and exponents, and radicals, and lots of other “cool” stuff…

Don’t worry. We’re not ready for that one…

yet!

xy

x

22164 36

Formulas are a type of equation.

Formulas are a type of equation. Recognize

these?

Formulas are a type of equation. Recognize

these?

d r t

Formulas are a type of equation. Recognize

these?

d r t

( )C F 5 329

Formulas are a type of equation. Recognize

these?

d r t

A l w

( )C F 5 329

Equations (and formulas) are used to represent real-world situations.

If you want to know what score you need on a semester exam to earn a particular final grade, we can write and solve an equation to find the answer.

We’ll solve this type of problem later this semester.

…equations can help us do magic

…equations can help us do magic!!

More on that later…

By the end of the semester, you will be able to:

By the end of the semester, you will be able to:•solve a multi-step equation, with variables

on both sides of the equal sign

By the end of the semester, you will be able to:•solve a multi-step equation, with variables

on both sides of the equal sign

( ) ( )b b 3 3 2 2 21

By the end of the semester, you will be able to:•solve a multi-step equation, with variables

on both sides of the equal sign

•represent real-world situations using equations

( ) ( )b b 3 3 2 2 21

By the end of the semester, you will be able to:•solve a multi-step equation, with variables

on both sides of the equal sign

•represent real-world situations using equations

•rewrite equations and formulas

( ) ( )b b 3 3 2 2 21

By the end of the semester, you will be able to:•solve a multi-step equation, with variables

on both sides of the equal sign

•represent real-world situations using equations

•rewrite equations and formulas

•determine how many solutions an equation has

( ) ( )b b 3 3 2 2 21

By the end of the semester, you will be able to:•solve a multi-step equation, with variables on

both sides of the equal sign

•represent real-world situations using equations

•rewrite equations and formulas

•determine how many solutions an equation has

•write your own “magic number” trick

( ) ( )b b 3 3 2 2 21

PLUS… we’re going to solve this challenging problem

PLUS… we’re going to solve this challenging problem

( ) x xx x x x x x x

3 1 112 24 9 15 25 6 512 3 7 20 54 3 200 20 36 9 4 7 21 64 2 33 3 3

PLUS… we’re going to solve this challenging problem

step – by – step

( ) x xx x x x x x x

3 1 112 24 9 15 25 6 512 3 7 20 54 3 200 20 36 9 4 7 21 64 2 33 3 3

PLUS… we’re going to solve this challenging problem

step – by – step

…and you ALREADY know how to simplify most of it!!

( ) x xx x x x x x x

3 1 112 24 9 15 25 6 512 3 7 20 54 3 200 20 36 9 4 7 21 64 2 33 3 3

Anyone up for the challenge?