Transcript More Inequalities

Inequalities
It is … Tuesday!!!
• Take out your homework and a red pen
• Period 2: Take out your notes from Friday!!!
• Take out your Review Packet and have it on
your desk
– Ms. Huls will walk around RIGHT when the bell
rings to see if you printed off the Review Packet
– It needs to be on your desk to get the full 5 points
3.1: Inequalities
Learning Objective
SWBAT solve inequalities
VOCAB
• inequality:
– a math sentence that contains the symbols
• Solution of an inequality
– Any number that makes the inequality true
Word Bank:
Translating Practice: Whiteboards
• a number y is greater than 4
___________________________
• a number c is less than or equal to 2
___________________________
• a number m is at least 3
___________________________
• In many states, you must be at least 16 years
old to obtain a driver’s license
• Ms. Huls makes more than 75 copies each day
Identifying Solutions
x> 6
X= 6
X=0
x= -4
Whiteboards
Graphing Inequalities
Graph c > -2
Graph 4 < m
Write an inequality from a Graph
Write an inequality from a Graph
Write an inequality from a Graph
• Equivalent inequality
– Inequalities with the same solution
• EX:
Solve each Inequality: Whiteboards
1. X-3 < 5
2. 12 < X -5
3. Y +5 < -7
Investigate!!!! Do this in your notes!
Answer all the questions
Red Flag Alert
When you multiply
or divide by a
negative number,
you need to FLIP the
inequality sign!
WHITEBOARDS
Write an inequality for each situation.
1. The temperature must be at least –10°F.
2. The temperature must be no more than 90°F.
x ≤ 90
Solve each equation.
3. x – 4 = 10
4. 15 = x + 1.1
14
13.9
x ≥ –10
Whiteboards
Solve each equation.
1. –5a = 30
2.
3.
4.
Graph each inequality.
5. x ≥ –10
6. x < –3
WHITEBOARDS!
Solve each inequality and graph the solutions.
1. 8x < –24
3.
x < –3
x > 20
2. –5x ≥ 30
4.
x ≤ –6
x≥6
PROBLEM SOLVING
Sami has a gift card. She has already used $14 of the of
the total value, which was $30. Write, solve, and graph
an inequality to show how much more she can spend.
1
Understand the Problem
The answer will be an inequality and a graph.
List important information:
• Sami can spend up to, or at most $30.
• Sami has already spent $14.
2
Make a Plan
Write an inequality.
Let g represent the remaining amount of money Sami can spend.
Amount
remaining
plus
g
+
g + 14 ≤ 30
amount used
14
is at most
≤
$30.
30
3
Solve
Since 14 is added to g, subtract 14 from
both sides to undo the addition.
g + 14 ≤ 30
– 14 – 14
g + 0 ≤ 16
g ≤ 16
It is not reasonable for Sami to spend a negative amount of money, so graph
numbers less than or equal to 16 and greater than 0.
0
2
4
6
8 10 12 14
16 18 10
Additional Example 3: Consumer Application
Mrs. Lawrence wants to buy an antique bracelet at an
auction. She is willing to bid no more than $550. So far,
the highest bid is $475. Write and solve an inequality to
determine the amount Mrs. Lawrence can add to the bid.
Check your answer.
Let x represent the amount Mrs. Lawrence can add to the bid.
$475
plus
475
+
475 + x ≤ 550
amount can
add
x
is at
most
≤
$550.
550
WORD PROBLEM!!!
Jill has a $20 gift card to an art supply store where 4 oz
tubes of paint are $4.30 each after tax. What are the
possible numbers of tubes that Jill can buy?
Let p represent the number of tubes of paint that Jill can buy.
$4.30
times
4.30
•
number of tubes
p
is at most
$20.00.
≤
20.00
Jill has a $20 gift card to an art supply store where 4 oz
tubes of paint are $4.30 each after tax. What are the
possible numbers of tubes that Jill can buy?
4.30p ≤ 20.00
Since p is multiplied by 4.30,
divide both sides by 4.30. The
symbol does not change.
p ≤ 4.65…
Since Jill can buy only whole numbers of tubes, she can buy 0, 1, 2, 3, or 4 tubes of
paint.
A pitcher holds 128 ounces of juice. What are the
possible numbers of 10-ounce servings that one pitcher
can fill?
Let g represent the number of servings of juice the pitcher can contain.
10 oz
times
number of
servings
is at most
128 oz
10
•
g
≤
128
A pitcher holds 128 ounces of juice. What are the possible numbers of 10-ounce
servings that one pitcher can fill?
10g ≤ 128
Since g is multiplied by 10, divide
both sides by 10.
The symbol does not change.
g ≤ 12.8
The pitcher can fill 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12 servings.
WHITEBOARDS
A soccer coach plans to order more
shirts for her team. Each shirt costs
$9.85. She has $77 left in her
uniform budget. What are the
possible numbers of shirts she can
buy?
Lesson Quiz: Part I
Solve each inequality and graph the solutions.
1. 13 < x + 7
x>6
2. –6 + h ≥ 15
h ≥ 21
3. 6.7 + y ≤ –2.1
y ≤ –8.8
Lesson Quiz: Part II
4. A certain restaurant has room for 120
customers. On one night, there are 72
customers dining. Write and solve an
inequality to show how many more people
can eat at the restaurant.
x + 72 ≤ 120; x ≤ 48, where x is a natural
number