Must show ALL steps and ALL work for credit Equations - Introduction.

Must show ALL steps and ALL work for credit

Equations - Introduction

VocabularyVocabulary

Equation Equation

Solution Solution

Inverse OperationInverse Operation

Insert Lesson Title Here

Course 2

1-10 Equations and Their Solutions

Ella has 22 CDs. This is 9 more than her friend Kay has.

This situation can be written as an equation.An equation is a mathematical statement that two expressions are equal in value.

An equation is like a balanced scale.

Right expressionLeft expression

Number of CDs Ella has

22

is equalto=

9 more thanKay hasj + 9

Course 2


Just as the weights on both sides of a balanced scale are exactly the same, the expressions on both sides of an equation represent exactly the same value.

When an equation contains a variable, a value of the variable that makes the statement true is called a solution of the equation.

22 = j + 9 j = 13 is a solution because 22 = 13 + 9.

22 = j + 9 j = 15 is not a solution because 22 15 + 9.

The symbol ≠ means “is not equal to.” Reading Math

Course 2


Determine whether the given value of the variable is a solution of t + 9 = 17.

Additional Example 1A: Determining Whether a Number is a Solution of an Equation

26

26 + 9 = 17?

35 = 17?

26 is not a solution of t + 9 = 17.

Substitute 26 for t.

t + 9 = 17

Course 2


Additional Example 1B: Determining Whether a Number is a Solution of an Equation

Determine whether the given value of the variable is a solution of t + 9 = 17.

8

8 + 9 = 17?

17 = 17?

8 is a solution of t + 9 = 17.

Substitute 8 for t.

t + 9 = 17

Course 2


LearnLearn to solve one-step equations. to solve one-step equations.

Sections 1.11 and 1.12 in textbook.Sections 1.11 and 1.12 in textbook.

Course 2

12-1 Solving Two-Step Equations

How to solve one-step equations

1. Goal – Get the variable alone2. Use the inverse operation to undo

On BOTH sides of the equationAddition and Subtraction are inverse operationsMultiplication and Division are inverse

operations**Remember – Whatever you do to one side you MUST do

to the other side!!!

2-Column NotesExample #1b + 2 = 6 Step 1

-2 -2 Step 2

b = 4 Step 3

Check 4 + 2 = 6 Step 4

6 = 6 Step 5

Instructions – STEPS

1) Copy Problem2) Inverse Operation

on BOTH sides*Do the Math!!!!

3) Solution – Box –in4) Check AnswerRewrite equation with Value substituted5) Do Math and check

BOTH sides

2-Column NotesExample #2n – 36 = 17 Step 1

+36 +36 Step 2

n = 53 Step 3

Check 53–36 = 17 Step 4

17 = 17 Step 5





BOTH sides

2-Column NotesExample #318 + j =94 Step 1

-18 -18 Step 2

j = 76 Step 3

Check 18+76=94 Step

4

94 = 94 Step 5





BOTH sides

2-Column NotesExample #4

Step 1 Step 2

Step 3 Step 4

Step 5





BOTH sides

9 108

9 108

9 912

9 12 108

108 108

q

q

q

check


Step 1 Step 2 Step 3 Step 4

Step 5





BOTH sides

135

5 13 55

65

6513

513 13

z

z

z

check


Step 1 Step 2

Step 3 Step 4

Step 5





BOTH sides

2211

11 22 1111242

24222

1122 22

w

w

w

check

When you solve equations that have one operation, you use an inverse operation toisolate the variable. You can also use inverseoperations to solve equations that have morethan one operation.

n + 7 = 15– 7 –7

n = 8

2x + 3 = 23

– 3 – 32x = 20 You need to use

another operationto isolate x.

It is often a good plan to follow the order of operations in reverse when solving equationsthat have more than one operation.

Course 2


LearnLearn to solve two-step equations. to solve two-step equations.

Course 2


Write down the directions to get to Pope High School from Hightower Trail MS parking lot.Directions to the

HSExplain how to

return to Hightower Trail MS.

Can you think of any other situations where you have to work backwards??????

How can the order of operations help us solve equations????List the order of

operations1.

2.

3.

4.

Now list it going backwards

1.

2.

3.

4.

Solve. Check each answer.

Additional Example 1A: Solving Two-Step Equations Using Division

9c + 3 = 39

9c + 3 = 39

– 3 –39c = 36

c = 4

Subtract 3 from both sides.

Divide both sides by 9.9c9

= 36 9

Course 2


Check.

Additional Example 1A Continued

9c + 3 = 39

9(4) + 3 39?=

?=

?=

36 + 3 39

39 39

Substitute 4 for c.

4 is a solution.

Course 2


Course 2


Reverse the order of operations when solving equations that have more than one operation.

Helpful Hint

Solve. Check the answer.

7c + 6 = 48

7c + 6 = 48

– 6 –67c = 42

c = 6


Divide both sides by 7.7c7

= 42 7

Check It Out: Example 1A

Course 2


Check It Out: Example 1A Continued


Check.

7c + 6 = 48

7(6) + 6 48?=

?=

?=

42 + 6 48

48 48

Substitute 6 for c.

6 is a solution.

Course 2


Solve.

Additional Example 2A: Solving Two-Step Equations Using Multiplication

6 + y5 = 21y5 = 216 +

– 6 –6y5

= 15

y5

= (5)15(5)

y = 75


Multiply both sides by 5.

Course 2


Solve.

Additional Example 2B: Solving Two-Step Equations Using Multiplication

x7 – 11 = 9

x7 – 11 = 9

x7 = 20

x7 = (7)20(7)

x = 140

Add 11 to both sides.


+11 +11

Course 2


Check It Out: Example 2A


Solve.

8 + y2 = 48y2 = 488 +

– 8 –8y2 = 40

y2

= (2)40(2)

y = 80



Course 2


Check It Out: Example 2B


Solve.

x5 – 31 = 19

x5 – 31 = 19

+31 +31x5 = 50

x5 = (5)50(5)

x = 250

Add 31 to both sides.


Course 2


Out ticket Show each step and number each stepSolve and Check

1. 4w – 3 = 25 2.

2 123

x

Must show ALL steps and ALL work for credit Equations - Introduction.

Documents

solution of t

value substituted5

given value

sides2column notesexample

variable alone2

balanced scale

additional example

mathematical statement