12/5/11

Bellringer: What is the greatest common factor of 30 and

45?

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Equations

Whatever you do to an equation, do the   SAME  thing to   BOTH   sides of that equation!

Start with adding/subtracting then do multiplying/dividing. (Reverse order of operations) To get a number to cross out, do the opposite operation.

You are trying to get x by itself to see what it equals!

Solve this equation for x:  x + 3 = 8

Check:  x + 3 = 8  5 + 3 = 8  8 = 8 true

Solve for x.

x-4=10

5x=25

X = 10

4

http://video.google.com/videoplay?docid=-799454014728007411#

To 6:40

Solve this equation for x:     5x - 2 = 13

Check:  5x - 2 = 13  5(3) - 2 = 13    15  - 2 = 13          13 = 13 true

2x – 4 = 8

5x + 10 = 80

-3x – 4 = -82

12/6/11

Get out your homework!Bellringer:

Add WITHOUT A CALCULATOR!!!

5+6

-10+4

-3+7

-5+(-4)

4+(-6)

5+(-2)

Homework Answers

1.x=4

2.k=12

3.n=12

4.z=6

2/3x + 2 = 8

x/5 + 2 = 8

Worksheet

Get the goof- What did the person do wrong?

Solve for x: 4x+12=76

-4 -4

x12=72

12 12

x = 6

Writing Equations

Add- more than, increases by, sum

Subtract- less, less than, difference, decreases by

Multiplication- product, twice, times

Division-quotient

Equals- is

Write in order of the words EXCEPT when it says less than! Switch the order for less than!

Worksheet

Write into an equation and then solve.

1. Four more than twice a number is 8

3. Five less than twice a number is 7

15. Eight more than the quotient of a number and 5 is 3

Video

http://video.google.com/videoplay?docid=-799454014728007411#

6:40

Solve this equation for x:  4x + 5 = x - 4

Check:  4x + 5 = x - 4  4(-3) + 5 = -3 -4     -12 + 5 = -7             -7 = -7 true

733 xx

119102 xx

1274 xx

7y + 5 - 3y + 1 = 2y + 2

Check:  7y + 5 - 3y + 1 = 2y + 2  7(-2) + 5 - 3(-2) + 1 = 2(-2) + 2         -14 + 5 + 6 + 1 = -4 + 2                            -2 = -2 true

3(n - 1.8) = 2n + 1

Check:    3(n - 1.8) = 2n + 1   3(6.4 - 1.8) = 2(6.4) + 1          3(4.6) = 12.8 + 1             13.8 = 13.8 true

An inequality is like an equation, but instead of an equal sign (=) it

has one of these signs:

< : less than≤ : less than or equal to

> : greater than≥ : greater than or equal to

Inequalities

Solve the exact same way, but it has a < or > instead of =

If you multiply or divide by a negative number, switch the sign!

When graphing, < and > are open circles and ≤ and ≥ are closed circles. Color everything x could be.

“x < 5”

means that whatever value x has, it must be less than 5.

Try to name ten numbers that are less than 5!

Numbers less than 5 are to the left of 5 on the number line.

0 5 10 15-20 -15 -10 -5-25 20 25

• If you said 4, 3, 2, 1, 0, -1, -2, -3, etc., you are right.• There are also numbers in between the integers, like 2.5, 1/2, -7.9, etc. • The number 5 would not be a correct answer, though, because 5 is not less than 5.

“x ≥ -2”

means that whatever value x has, it must be greater than or

equal to -2.

Try to name ten numbers that are greater than or equal to -

2!

Numbers greater than -2 are to the right of 5 on the number line.

0 5 10 15-20 -15 -10 -5-25 20 25

• If you said -1, 0, 1, 2, 3, 4, 5, etc., you are right.• There are also numbers in between the integers, like -1/2, 0.2, 3.1, 5.5, etc. • The number -2 would also be a correct answer, because of the phrase, “or equal to”.

-2

ExamplesGraph x > 7

Graph -4 ≥ x

Since the sign is >, we put an OPEN circle on 7. X is greater than 7 so we color up the number line.

Since the sign is ≥ we put a CLOSED circle on -4. X is smaller than -4 so we color down the number line.

Solving One-Step Inequalities

53 x

6) Solve x -14 < 16 x - 14 < 16

+ 14 + 14

x < 30

30 -14 = 16

16 = 16

Solve this problem like an equation

1. Draw “the line”2. Add 14 to both sides3. Simplify4. Check your answer5. Graph the solution

o30 3129

8) Solve 8y + 3 > 9y - 14

o17 1816

- 8y - 8y

3 > y - 14

+ 14 + 14

17 > y

y < 178(17) + 3 = 9(17) - 14

1. Draw “the line”

2. Subtract 8y from both sides

3. Simplify

4. Add 14 to both sides

5. Simplify

6. Rewrite inequality with the variable first

7. Check your answer

8. Graph the solution

Solve for x:  (x/3) > -4

Solve for x:  6x > 36

Inequalities

If you multiply or divide by a negative number, the sign changes!

Examples of when to switch signs

-3x+4 > 21

X – 7 < 45

-2

Solving One-Step Inequalities

73

x

Writing Inequalities

You have at least 35 minutes to complete your quiz.

The speed limit is 55 mph.

At the most, you can spend $50.

Worksheet

Metropolis Gas and Power charges their customers a monthly service charge of $13.60 and a volume charge of $1.59 for every 100 cubic feet of natural gas used. Which of the following equations could be used to find Bruce Wayne's monthly gas bill?

(Let x represent the number of cubic feet of gas used in hundreds and y represent the total monthly cost.)

 7 - x < 6

What is the first step when solving the equation for x? (1/5) (6x + 4) = 4x

  Solve for x. x/4 - 9 = 5

Study Islandwww.studyisland.com

Click on Nolan Period ____

Click on equations.

Complete 10 questions in test mode.

When you finish with equations work on Inequalities. Turn scratch paper into basket.

This is a grade!!!!

Test on Monday!