Download Inequalities H.notebook

Inequalities H.notebook
September 27, 2016
What Does the Prefix "In" mean when added to a word?
Solving Inequalities
An inequality is a number sentence much like an
equation, but rather than an equal sign in the middle,
there is...
>
<
≥
≤
The solution to an equation looks like...
x=3
The solution to an inequality looks like
x<5
In both cases, the solution makes the number
sentence a true statement.
Inequalities H.notebook
September 27, 2016
Solutions to Inequalities
The number of cars in the parking lot is greater
than 5.
c>5
How many possible numbers for c make a true
statement?
Is the number a solution of
2x + 1 > -3
A. -3
B. -1
The symbols...
and the words which imply them.
<
>
less than greater than
below
fewer than
≤
less/equal
more than
at most
above
no more than
Exceeds
up to and
including
≥
greater/equal
at least
no less than
at minimum
Inequalities H.notebook
September 27, 2016
Practice writing the inequalities
1.
There is more than 21 pilots in the airport.
2.
I ate at most 43 cookies in one sitting.
3.
The fire was burning on all floors below the
7th.
4.
She will receive no less than an 81 on her test.
5.
There were fewer than 4 officers at the scene.
Graphing Inequalities on a Number Line
Inequality
<
>
≥
≤
Symbol
I ran no more than 13 miles.
I walked less than 2 miles.
Inequalities H.notebook
September 27, 2016
Write the inequality represented by the graph.
-3
4
27
-11
Practice problems
Are the numbers solutions to the inequalities?
1.
4x + 1 < 13
5
0
3
2.
-3x + 5 ≥ 2
-2
2
1
Write the inequality and graph.
3.
I watched no less than 10 episodes.
4.
Berkeley ran the ball fewer than 24 times.
5.
We traveled at most 900 miles.
Inequalities H.notebook
September 27, 2016
Grab a Calculator
Take out Your Notebook
Bell Ringer
Write the inequality to represent the situation and graph on a number line.
There are no more than 11 characters
in the movie.
Solving Inequalities
So remember that whole "solving equations" thing
we did? Well it hasn't gone anywhere, and it's only
coming back!
We solve inequalities the same way as we solved
equations, using _____________ _____________ .
x + 4 > -8
Check your
answer!!!
Inequalities H.notebook
September 27, 2016
1.
x - 5 ≤ 19
2.
x -10 > -1
3.
x+9<6
One Rule to Note!!!
When multiplying or dividing both sides of inequality
by a NEGATIVE number, you MUST FLIP the
inequality symbol.
-4x ≥ 8
Inequalities H.notebook
September 27, 2016
1.
-5x > 30
2.
4x + 2 < 22
3.
-7x ≥ 42
4.
9 - x ≤ 11
The graph below represents which inequality?
-6
A.
x > -6
B.
x < -6
C.
x < -6
D.
x > -6
Inequalities H.notebook
September 27, 2016
6 - 4x > -30
A. x > -9
B. x > 9
C. x < -9
D. x < 9
Solve Multi-Step Inequalities
Once again, we will solve multi-step inequalities just as
we solved multi-step equations.
4x + 3 > -x + 13
Solve and graph the solutions to the inequalities.
1.
-2x - 8 < -5x + 25
2.
3(x - 4) ≥ 7x + 8
Inequalities H.notebook
September 27, 2016
Grab a Calculator
Take out Your Notebook
Bell Ringer
Answer the inequality below in your notebook...
-5x > 40
A. x > 8
B. x > -8
C. x < 8
Solve the Inequalities
1. 6(x + 3) > -36
2. 4x - 8 > 6x + 24
D. x < -8
Inequalities H.notebook
September 27, 2016
Name _____________
Solve the Multi-Step Equations and sketch the
solutions
1.
4x - 3 < 2x + 21
2.
-6x + 2 > x + 16
3.
-x + 10 > - 5x +2
Word Problems: Defining a Variable
When turning a word problem into an equation/
inequality we need to determine what the variable
will be.
Tommy has $40 in his wallet. He will spend two
dollars on burgers. He has at least eight dollars
left. What is the maximum amount of burgers he
could have bought?
The variable will be the object(s) asked for in the
question.
Inequalities H.notebook
Rate
September 27, 2016
Constant
Total
Word Problems Featuring Inequalities
Your cell plan costs $40.00 a month plus $.14 for each text message you send or receive. You have at most $45 to spend on your cell phone bill. 1.
Write an equation which represents this scenario.
2.
What is the maximum number of texts you can send.
3.
Explain your answer to number 2.
Inequalities H.notebook
September 27, 2016
A used car is going to cost Chasity at least $555. She has managed to save up $222. If her job pays her $15 an hour, how many hours must she work in order to be able to afford the car?
1.
Write an equation which represents this scenario.
2.
What is the minimum number of whole number hours
she can work?
A.
h ≥ 22
B.
h ≤ 22
C.
h ≥ 23
D.
h ≤ 23
Grab a Calculator
Bell Ringer
Answer the inequality below in your notebook...
3x + 2 > 4x + 8
A. x > -6
B. x > 6
C. x < -6
D. x < 6
Inequalities H.notebook
September 27, 2016
Grab a Calculator
Take out Your Notebook
Bell Ringer
Answer the inequality below in your notebook...
-5x > 40
A. x > 8
B. x > -8
C. x < 8
D. x < -8
Compound Inequalities
A compound inequality consists of two distinct
inequalities joined by the word and or the word or.
And Inequality
Or Inequality
4
9
4
x > 10
x>4
9
x > 4 and x < 9
4<x<9
x<9
10
x<2
2
2
10
x < 2 or x > 10
Inequalities H.notebook
September 27, 2016
Graph the inequalities
1. x > 3 and x < 11
2. x < -1 or x > 4
3. 7 < x < 12
Solving Compound "And" Inequalities
3 < m + 8 < 12
Inequalities H.notebook
September 27, 2016
-3 < x-4 < -1
-8 < 2y-6 < -2
Inequalities H.notebook
September 27, 2016
Solving Compound "Or" Inequalities
x+5<1
3x - 1 < 11
4x > 8
or
or
2x > 10
Inequalities H.notebook
September 27, 2016
To achieve a B in your college English class, you must
achieve a test average between 84 and 86. You scored 86,
85, and 80 on the first three exams. What possible scores
can you earn on the fourth and final to earn a B.
What are the solutions of
3x + 2 < -7
OR
-4x + 5 < 1
Inequalities H.notebook
September 27, 2016
Solve and Graph
5x + 1 < 11
AND
6x > 30
Bell Ringer
Get a Calculator
Solve and Graph the Results
6 < 3x + 9 ≤ 15
Inequalities H.notebook
September 27, 2016
Interval Notation
When writing the solution set to an inequality, we may
choose to use, (or be asked to use), interval notation.
An interval is a portion of the number line.
Parenthesis - Use parentheses when < or > are used to
describe an interval's endpoint.
Brackets - Use brackets when < or > are used to describe an
interval's endpoints.
Infinty - Use ∞ when the interval continues off in a positive
direction. Use -∞ when the interval continues off in a
negative direction.
Solve, graph, and use interval notation to describe the solution.
1.
3 < 4x - 5 < 15
2.
5x - 3 > 7
3.
-9 < 3m + 6 < 18
OR
4x - 6 < -10
Inequalities H.notebook
September 27, 2016
Domain and Range
Domain
Range
Domain
Range
Inequalities H.notebook
September 27, 2016
Domain
Range
Write the inequality which represents the word sentence.
1. There are at least 20 kittens in the box.
2. I’m going to eat less than 20 of those kittens.
3. The number of kittens I ate exceeds 13.
Graph the inequalities.
4. x < 8
5. x ≥ ‐1
6. 6 ≤ x
Solve the inequalities. Graph their solutions.
7. x + 5 > 8
≤ 6
10. 4x – 8 < 8x + 12
12. ‐29 < 9x ‐ 2
8. ‐5x < 20
11. 6x – 4 ≥ 8
9.
Inequalities H.notebook
September 27, 2016
­2 < 2x + 6 < 16
Solve
Graph
Interval Notation
Bell Ringer
Shane wants to get into Harvard. He needs more than
a 91 average in History to get into their history
program. So far, his test grades are 89, 93, and 85.
He has one more test to take. Write and solve the
inequality to determine what he must score in order to
meet his goal.
Inequalities H.notebook
September 27, 2016
Absolute Value
The absolute value of a number is
the distance the number is from zero.
0
-6
4
-6 = 6
4
=4
A "distance" can't be negative.
Solving Absolute Value Equations
x + 2= 9
0
x + 2= 9
Inequalities H.notebook
September 27, 2016
An absolute value
problem will
always have
Two Answers
x -2 =9
Note: Make sure the
abs val is by itself
before you split up the
problem.
Inequalities H.notebook
2x + 4 - 5 = 7
-3 4x = -36
September 27, 2016
Inequalities H.notebook
September 27, 2016
2 x +4 -8 =2
x + 2 = -6
Inequalities H.notebook
September 27, 2016
Practice Problems
x -5 =4
x -3
= 10
2x + 6 = 12
3 x + 6 - 12 = 9