Transcript 5.1 - TeacherWeb

Warm-Up Exercises
1. Is –9 a solution of a + 7 = –2?
ANSWER
yes
2. Solve the equation h + 12 = –8.
ANSWER
–20
Warm-Up Exercises
3. Write an inequality that describes the number of
CDs you can buy for $12 each if you have no more
than $60 to spend. Can you buy 6 CDs?
ANSWER
12x ≤ 60; no
Warm-Up1Exercises
EXAMPLE
Write and graph an inequality
Death Valley
The highest temperature recorded in the United States
was 134°F at Death Valley, California, in 1913. Use
only this fact to write and graph an inequality that
describes the temperatures in the United States.
SOLUTION
Let T represent a temperature (in degrees Fahrenheit)
in the United States. The value of T must be less than
or equal to 134. So, an inequality is T ≤ 134.
Warm-Up2Exercises
EXAMPLE
Write inequalities from graphs
Write an inequality represented by the graph.
a.
SOLUTION
a.
The open circle means that –6.5 is not a solution of
the inequality. Because the arrow points to the
right, all numbers greater than –6.5 are solutions.
ANSWER
An inequality represented by the graph is x > –6.5.
Warm-Up2Exercises
EXAMPLE
Write inequalities from graphs
b.
SOLUTION
b.
The closed circle means that 4 is a solution of the
inequality. Because the arrow points to the left, all
numbers less than 4 are solutions.
ANSWER
An inequality represented by the graph is x ≤ 4.
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 1 and 2
Write an inequality represented by the graph.
ANSWER
x ≥ –2.5
Warm-Up3Exercises
EXAMPLE
Solve an inequality using addition
Solve x – 5 > –3.5. Graph your solution.
x – 5 > –3.5
x – 5 + 5 > –3.5 + 5
x > 1.5
Write original inequality.
Add 5 to each side.
Simplify.
ANSWER
The solutions are all real numbers greater
than 1.5. Check by substituting a number
greater than 1.5 for x in the original
inequality.
Warm-Up3Exercises
EXAMPLE
Solve an inequality using addition
CHECK
x – 5 > –3.5
?
6 – 5 > –3.5
1 > –3.5
Write original inequality.
Substitute 6 for x.
Solution checks.
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 3
Solve the inequality. Graph your solution.
4. x – 9 ≤ 3
ANSWER
x ≤ 12
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 3
Solve the inequality. Graph your solution.
5.
p – 9.2 < –5
ANSWER
p < 4.2
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 3
Solve the inequality. Graph your solution.
6. –1 ≥ m – 1
2
ANSWER
m≤ –1
2
EXAMPLE
Warm-Up5Exercises
Solve a real-world problem
LUGGAGE WEIGHTS
You are checking a bag at an airport. Bags can weigh
no more than 50 pounds. Your bag weighs 16.8 pounds.
Find the possible weights w (in pounds) that you can
add to the bag.
SOLUTION
Write a verbal model. Then write and solve an
inequality.
16.8
+
w
≤
50
EXAMPLE
Warm-Up5Exercises
Solve a real-world problem
16.8 + w ≤ 50
16.8 + w – 16.8 ≤ 50 – 16.8
w ≤ 33.2
Write inequality.
Subtract 16.8 from each side.
Simplify.
ANSWER
You can add no more than 33.2 pounds.
Warm-Up
Exercises
GUIDED
PRACTICE
7.
for Examples 4 and 5
Solve y + 5.5 > 6. Graph your solution.
ANSWER
y > 0.5
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 4 and 5
8. WHAT IF? In Example 5, suppose your bag weighs 29.1
pounds. Find the possible weights (in pounds) that you
can add to the bag.
ANSWER
w ≤ 20.9 lb
Warm-Up Exercises
Warm-up: Page 296 #1-19 all
Homework: Page 301 #3-28 all
Warm-Up
Example
1 Exercises
Antarctica
The lowest temperature recorded in Antarctica was
–129°F at the Russian Vostok station in 1983. Use only
this fact to write and graph an inequality that
describes the temperatures in Antarctica.
ANSWER
x ≥ –129°F
Warm-Up
Exercises
GUIDED
PRACTICE
Write an inequality represented by the graph.
ANSWER
x<8
Daily
Homework
Quiz
Warm-Up
Exercises
Solve the inequality. Graph your solution.
3.
s + 0.5 ≥ –1.5
ANSWER
all real numbers greater than or equal
to –2
4. k – 6 < –5
ANSWER
all real numbers less than 1
EXAMPLE
Warm-Up5Exercises
Solve an inequality using subtraction
Solve 9 ≥ x + 7. Graph your solution.
9≥x+7
9–7≥x+7–7
2≥x
Write original inequality.
Subtract 7 from each side.
Simplify.
ANSWER
You can rewrite 2 ≥ x as x ≤ 2.
The solutions are all real
numbers less than or equal
to 2.
Daily
Homework
Quiz
Warm-Up
Exercises
6.
A theater can seat at most 625 people. The box
office has sold tickets for 284 seats. Write and
solve an inequality to find the possible numbers of
remaining tickets t the box office can sell.
ANSWER
t + 284 ≤ 625; t ≤ 341;
no more than 341 tickets.