Download Unit 1-6

Five-Minute Check (over Lesson 1–5)
CCSS
Then/Now
New Vocabulary
Key Concept: “And” Compound Inequalities
Example 1: Solve an “And” Compound Inequality
Key Concept: “Or” Compound Inequalities
Example 2: Solve an “Or” Compound Inequality
Example 3: Solve Absolute Value Inequalities
Key Concept: Absolute Value Inequalities
Example 4: Solve a Multi-Step Absolute Value Inequality
Example 5: Real-World Example: Write and Solve an
Absolute Value Inequality
Over Lesson 1–6
1–5
Solve the inequality 3x + 7 > 22. Graph the solution
set on a number line.
Solve the inequality 3(3w + 1) ≥ 4.8. Graph the
solution set on a number line.
Solve the inequality 7 + 3y > 4(y + 2). Graph the
solution set on a number line.
Solve the inequality
. Graph the solution
set on a number line.
A company wants to make at least $255,000 profit
this year. By September, the company made
$127,500 in profit. The company plans to earn, on
average, $15,000 each week in profit. Will the
company reach its goal by the end of the year?
Over Lesson 1–6
1–5
Solve the inequality 3x + 7 > 22. Graph the solution
set on a number line.
A. {x | x > 5}
B. {x | x < 5}
C. {x | x > 6}
D. {x | x < 6}
Over Lesson 1–6
1–5
Solve the inequality 3(3w + 1) ≥ 4.8. Graph the
solution set on a number line.
A. {w | w ≤ 0.2}
B. {w | w ≥ 0.2}
C. {w | w ≥ 0.6}
D. {w | w ≤ 0.6}
Over Lesson 1–6
1–5
Solve the inequality 7 + 3y > 4(y + 2). Graph the
solution set on a number line.
A. {y | y > 1}
B. {y | y < 1}
C. {y | y > –1}
D. {y | y < –1}
Over Lesson 1–6
1–5
Solve the inequality
set on a number line.
A. {w | w ≤ –9}
B. {w | w ≥ –9}
C. {w | w ≤ –3}
D. {w | w ≥ –3}
. Graph the solution
Over Lesson 1–6
1–5
A company wants to make at least $255,000 profit
this year. By September, the company made
$127,500 in profit. The company plans to earn, on
average, $15,000 each week in profit. Will the
company reach its goal by the end of the year?
A. yes
B. no
Mathematical Practices
5 Use appropriate tools strategically.
You solved one-step and multi-step inequalities.
• Solve compound inequalities.
• Solve absolute value inequalities.
• compound inequality
• intersection
• union
There are six possibilities:
“And”
“Or”
“And” or “Or”
“And” or “Or”
“And” No solution
“Or” All Real Numbers
Solve an “And” Compound Inequality
Solve 10  3y – 2 < 19. Graph the solution set on a
number line.
Method 1 Solve separately.
Write the compound inequality using the
word and. Then solve each inequality.
10  3y – 2
and
3y – 2 < 19
12  3y
3y < 21
4 y
y<7
4y<7
Solve an “And” Compound Inequality
Method 2 Solve both together.
Solve both parts at the same time by
adding 2 to each part. Then divide each
part by 3.
10  3y – 2 < 19
12 
3y
< 21
4
y
<7
Solve an “And” Compound Inequality
Graph the solution set for each inequality and find their
intersection.
y4
y<7
4y<7
Answer: The solution set is y | 4  y < 7.
What is the solution to 11  2x + 5 < 17?
A.
B.
C.
D.
Solve an “Or” Compound Inequality
Solve x + 3 < 2 or –x  –4. Graph the solution set on
a number line.
Solve each inequality separately.
x+3 <2
x < –1
or
–x  –4
x4
x < –1
x4
x < –1 or x  4
Answer: The solution set is x | x < –1 or x  4.
What is the solution to x + 5 < 1 or –2x  –6?
Graph the solution set on a number line.
A.
B.
C.
D.
Solve Absolute Value Inequalities
A. Solve 2 > |d|. Graph the solution set on a
number line.
2 > |d| can be re-written |d| < 2. From the definition of
absolute value this means that the distance between
d and 0 on a number line is less than 2 units.
Notice that the graph of
|d| < 2 is the same as the
graph of d > –2 and d < 2.
All of the numbers between –2 and 2 are less than
2 units from 0.
Answer: The solution set is d | –2 < d < 2.
Solve Absolute Value Inequalities
B. Solve |d| > 3. Graph the solution set on a
number line.
|d| > 3 means the distance between d and 0 is greater
than 3 units.
Notice that the graph of
|d| > 3 is the same as the
graph of d < –3 or d > 3.
All of the numbers not between –3 and 3 are greater
than 3 units from 0.
Answer: The solution set is d | d < –3 or d > 3.
A. What is the solution to |x| > 5?
A.
B.
C.
D.
B. What is the solution to |x| < 5?
A. {x | x > 5 or x < –5}
B. {x | –5 < x < 5}
C. {x | x < 5}
D. {x | x > –5}
Solve a Multi-Step Absolute Value Inequality
Solve |2x – 2|  4. Graph the solution set on a
number line.
|2x – 2|  4 is equivalent to 2x – 2  4 or 2x – 2  –4.
Solve each inequality.
2x – 2  4
or
2x – 2  –4
2x  6
2x  –2
x3
x  –1
Answer: The solution set is x | x  –1 or x  3.
What is the solution to |3x – 3| > 9? Graph the
solution set on a number line.
A.
B.
C.
D.
Write and Solve an Absolute Value
Inequality
A. JOB HUNTING To prepare for a job interview,
Hinda researches the position’s requirements and
pay. She discovers that the average starting salary
for the position is $38,500, but her actual starting
salary could differ from the average by as much as
$2450. Write an absolute value inequality to
describe this situation.
Let x = the actual starting salary.
The starting salary can differ
by as much as $2450.
from the average
|38,500 – x|
Answer: |38,500 – x|  2450

2450
Write and Solve an Absolute Value
Inequality
B. JOB HUNTING To prepare for a job interview,
Hinda researches the position’s requirements and
pay. She discovers that the average starting salary
for the position is $38,500, but her actual starting
salary could differ from the average by as much as
$2450. Solve the inequality to find the range of
Hinda’s starting salary. | x – 38,500 |  2450
Rewrite the absolute value inequality as a compound
inequality. Then solve for x.
–2450  x – 38,500  2450
–2450 + 38,500 
x
 2450 + 38,500
36,050 
x
 40,950
Write and Solve an Absolute Value
Inequality
Answer: The solution set is x | 36,050  x  40,950.
Hinda’s starting salary will fall within $36,050
and $40,950.
A. HEALTH The average birth weight of a newborn
baby is 7 pounds. However, this weight can vary by
as much as 4.5 pounds. What is an absolute value
inequality to describe this situation?
A. |4.5 – w|  7
B. |w – 4.5|  7
C. |w – 7|  4.5
D. |7 – w|  4.5
B. HEALTH The average birth weight of a newborn
baby is 7 pounds. However, this weight can vary by
as much as 4.5 pounds. What is the range of birth
weights for newborn babies?
A. {w | w ≤ 11.5}
B. {w | w ≥ 2.5}
C. {w | 2.5 ≤ w ≤ 11.5}
D. {w | 4.5 ≤ w ≤ 7}