Wednesday, September 4th

Please complete the warm up

1. Solve: -(x+3)=5 + 2(4x-20)

2. Solve:

2465

1 xx

Joke of the Day

How do equations get into shape?!?!

They do multi-step aerobics

Homework Answers

Around the World

Fraction Coefficients

1.

2.

3.

525

7x

21 9

3k

84 319w

Don’t forget to:

FLIPThe

coefficient

What Did the Superman Do Wrong?!?!

-(x – 4) = -3x - 7 + 5x

-x – 4 = 8x + 7

-4=7x + 7

-11 = 7x

-11/7 = x

What Did the Sponge Bob Do Wrong?!?!

312

4x

1 3

12 4x

3

48x

Helpful Hint

Equations are often easier to solve when the variable has a positive coefficient. Keep this in mind when deciding on which side to "collect" variable terms.

Let’s Practice

What would I do to keep the coefficient Positive?

1. 7a – 17 = 4a + 12. 2b – 5 = 8b + 1 3. 4x – 2 = 3x + 44. 2x -5 = 4x – 1 5. 5x + 2 = 3x

You’ve got to Practice!

Let’s get warmed Up!

1. –4 + 7x = 3

2. 6 – 7(a + 1) = –3(2 – a

3.

4 – 6a + 4a = –1 – 5(7 – 2a)

Challenge Problem

Combine like terms.

Distribute –5 to the expression in parentheses.

4 – 6a + 4a = –1 –5(7 – 2a)

4 – 6a + 4a = –1 –5(7) –5(–2a)

4 – 6a + 4a = –1 – 35 + 10a

4 – 2a = –36 + 10a

+36 +36

40 – 2a = 10a+ 2a +2a

40 = 12a

Since –36 is added to 10a, add 36 to both sides.

To collect the variable terms on one side, add 2a to both sides.

ANY QUESTIONS BEFORE WE GO FURTHER…..

Graphing and Solving Inequalities

1. An inequality is a statement that two quantities are not equal. The quantities are compared by using the following signs:

≤A ≤ B

A is less than or

equal to B.

<A < B

A is lessthan B.

>A > B

A is greaterthan B.

≥A ≥ B

A is greaterthan or

equal to B.

≠A ≠ B

A is notequal to B.

2. A solution of an inequality is any value that makes the inequality true.

Vocabulary

An inequality like x < 6 has too many solutions to list. You can use a graph on a number line to show all the solutions.

The solutions are shaded and an arrow shows that the solutions continue past those shown on the graph. To show that an endpoint is a solution, draw a solid circle at the number. To show an endpoint is not a solution, draw an empty circle.

Graphing Inequalities

Don't Shade Shade< Less than

Example: x<4

> Greater than

Example: x > 5

≤ Less than OR equal to

Example: x ≤5

≥ Greater than OR equal to

Example: x ≥6

To Shade or Not to Shade

o

o

Words ExampleD: Draw a number line

and a circle at the endpoint

I: Include? To shade or not to shade!

S: Shade in the correct direction

C: Check: substitute a value on the solution and check to see if it’s true

x <4

D:

I:

S:

Check: Is -5 less than 4?

Steps to Graphing Inequalities: DISC

o

Example of Graphing Inequalities

Graph each inequality.

A. m ≥

0 1– 2 3 3

Draw a solid circle at .

Shade all the numbers

greater than and draw an

arrow pointing to the right.B. t < 5(–1 + 3)

t < 5(–1 + 3)

t < 5(2)

t < 10

–4 –2 0 2 4 6 8 10 12 –6 –8

Simplify.

Draw an empty circle at 10.Shade all the numbers less than 10 and draw an arrow pointing to the left.

Reading Math

•“No more than” means “less than or equal to.”

•“At least” means “greater than or equal to”.

Page 31 IMN

Solving one-step inequalities is much like solving one-step equations. To solve an inequality, you need to isolate the variable using the properties of inequality and inverse operations.

Guess What?!?!

Using Addition and Subtraction to Solve Inequalities

Solve the inequality and graph the solutions.

x + 12 < 20

x + 12 < 20

–12 –12

x + 0 < 8

x < 8

Since 12 is added to x, subtract 12 from both sides to undo the addition.

–10 –8 –6 –4 –2 0 2 4 6 8 10

Draw an empty circle at 8.

Shade all numbers less than 8 and draw an arrow pointing to the left.

Multiplying or Dividing by a Positive Number

Solve the inequality and graph the solutions.

7x > –42

7x > –42

>

1x > –6

Since x is multiplied by 7, divide both sides by 7 to undo the multiplication.

x > –6

–10 –8 –6 –4 –2 0 2 4 6 8 10

r < 16

0 2 4 6 8 10 12 14 16 18 20

Since r is multiplied by ,

multiply both sides by the

reciprocal of .

Multiplying or Dividing by a Positive Number

Solve the inequality and graph the solutions.

MOST IMPORTANT

PART OF TODAY!!!!!!!!!!

If you multiply or divide both

sides of an inequality by a negative number, the resulting inequality is not a

true statement. You need to reverse the inequality symbol to make the statement true.

Multiplying or Dividing by a Negative Number

Solve the inequality and graph the solutions.–12x > 84

x < –7

Since x is multiplied by –12, divide both sides by –12. Change > to <.

–10 –8 –6 –4 –2 0 2 4 6–12–14

–7

Caution! Do not change the direction of the inequality symbol just because you see a negative sign. For example, you do not change the symbol when solving 4x < –24.

I. Solving Multi-Step InequalitiesPage 5 IMN

Solve the inequality and graph the solutions.

45 + 2b > 61

45 + 2b > 61–45 –45

2b > 16

b > 8

0 2 4 6 8 10 12 14 16 18 20

Since 45 is added to 2b, subtract 45 from both sides to undo the addition.

Since b is multiplied by 2, divide both sides by 2 to undo the multiplication.

#1

8 – 3y ≥ 298 – 3y ≥ 29–8 –8

–3y ≥ 21

y ≤ –7

Since 8 is added to –3y, subtract 8 from both sides to undo the addition.

Since y is multiplied by –3, divide both sides by –3 to undo the multiplication. Change ≥ to ≤.

–10 –8 –6 –4 –2 0 2 4 6 8 10

–7

#2

KeepPracticing

!

–12 ≥ 3x + 6–12 ≥ 3x + 6– 6 – 6

–18 ≥ 3x

–6 ≥ x

Since 6 is added to 3x, subtract 6 from both sides to undo the addition.

Since x is multiplied by 3, divide both sides by 3 to undo the multiplication.

–10 –8 –6 –4 –2 0 2 4 6 8 10

#3

x≤-6

Make sure variable is on

the left!!!

x < –11

–5 –5x + 5 < –6

–20 –12 –8 –4–16 0

–11

Since x is divided by –2, multiply both sides by –2 to undo the division. Change > to <.

Since 5 is added to x, subtract 5 from both sides to undo the addition.

#4You try!!!

3 + 2(x + 4) > 33 + 2(x + 4) > 3

3 + 2x + 8 > 3

2x + 11 > 3– 11 – 11

2x > –8

x > –4

Distribute 2 on the left side.

Combine like terms.Since 11 is added to 2x, subtract

11 from both sides to undo the addition.

Since x is multiplied by 2, divide both sides by 2 to undo the multiplication.

–10 –8 –6 –4 –2 0 2 4 6 8 10

#5You try!!!Take it step by step