Name
Lesson
2-1
Date
Class
Ready To Go On? Skills Intervention
Graphing and Writing Inequalities
Find these vocabulary words in the lesson and the Multi-Language Visual Glossary.
Vocabulary
inequality
solution of an inequality
Graphing Inequalities
1  ​
A. b # 7​ __
2
What does the # symbol indicate?
1  ​included in the solution set?
Is 7​ __
2
1  ​be solid or empty?
Should the circle drawn at 7​ __
2
In which direction should the arrow point?
Graph the inequality.
–2 –1 0 1 2 3 4 5 6 7 8
B. r . 23
What does the . symbol indicate?
Is 23 included in the solution set?
So, a(n)
Graph the inequality.
circle should be used and the arrow should point to the
.
–5 –4 –3 –2 –1 0 1 2 3 4 5
Writing an Inequality from a Graph
A.
–5 –4 –3 –2 –1 0 1 2 3 4 5
B.
–5 –4 –3 –2 –1 0 1 2 3 4 5
Which direction does the arrow point? Which direction does the arrow point?
What does the solid circle mean? What does the empty circle mean?
Which symbol should be used?
Which symbol should be used?
Write the inequality. Write the inequality.
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19
Holt McDougal Algebra 1
Name
Lesson
Date
Class
Ready To Go On? Skills Intervention
2-2 Solving One-Step Inequalities by Adding or Subtracting
Using Addition and Subtraction to Solve Inequalities
Solve each inequality and graph the solutions.
A. y 1 4 # 9
Step 1: Solve for y.
Step 2: Graph the solution.
y 1 4 # 9To isolate y,
2
4 from both sides of the inequality.
2
y#
A(n)
Find the value of y.
circle should be used and the arrow should point to the
.
–5 –4 –3 –2 –1 0 1 2 3 4 5
B. x 2 9 $ 27
Step 1: Solve for x.
Step 2: Graph the solution.
x 2 9 $ 27
1
Isolate x by
9 to both sides of the inequality.
1
x$
A(n)
circle should be used and the arrow should point to the
.
–5 –4 –3 –2 –1 0 1 2 3 4 5
C. 5 . p 2 4
Step 1: Solve for p.
Step 2: Graph the solution.
5 . p 2 4
1
Isolate p by
4 to both sides of the inequality.
1
.p
Another way to write this inequality is p ,
A(n)
.
circle should be used and the arrow should point to the
.
–10 –8 –6 –4 –2 0 2 4 6 8 10
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20
Holt McDougal Algebra 1
Name
Lesson
Date
Class
Ready to Go On? Problem Solving Intervention
2-2 Solving One-Step Inequalities by Adding or Subtracting
Solving one-step inequalities is much like solving one-step equations.
Kendra receives a weekly allowance of $15.00. She has already spent $11.50 on a
movie ticket and a bag of popcorn. Write and solve an inequality to determine how
much money Kendra can spend the rest of the week.
Understand the Problem
1. How much allowance does Kendra receive?
2. How much has Kendra spent so far this week?
Make a Plan
3. What do you need to determine?
4. What inequality symbol represents less than or equal to?
Solve
5. Let s represent the amount of money Kendra can spend the rest of the week.
Write an inequality to represent the situation.
The amount left
to spend
is less than
or equal to
1
$11.50
1
$11.50
$15.00
$15.00
6. Solve for s by subtracting 11.50 from both sides of the inequality. s #
7. The amount of money Kendra can spend the rest of the week is at most .
8. What is the least amount of money that Kendra can spend?
Look Back
9. Graph your solution on the number line. –5 –4 –3 –2 –1 0 1 2 3 4 5
10. Choose a number that is included in your solution.
11. Substitute this number for s into the inequality you wrote in Exercise 5.
12. Does the number you chose in Exercise 10, make the inequality true or false?
13. Does your solution make sense?
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21
Holt McDougal Algebra 1
Name
Lesson
Date
Class
Ready To Go On? Skills Intervention
2-3 Solving One-Step Inequalities by Multiplying or Dividing
Multiplying or Dividing by a Positive Number
2  ​y # 24. Then graph the solutions.
Solve ​ __
5
The variable, y, is being multiplied by
reciprocal of
, so you need to multiply by the
on both sides of the inequality.
Step 1: Solve for y.
2  ​y # 24
​ __
5
2  ​y # 24 ?
? ​ __
5
____
y # ​ 220
 ​ 
 
2
y#
5  ​.
both sides of the inequality by ​ __
2
Isolate y by
Divide.
Step 2: Graph the solution. –16–14 –12 –10 –8 –6 –4 –2
A(n)
0
2
circle should be used and the arrow should point to the
.
Multiplying or Dividing by a Negative Number
A. Solve 26x , 36.
Isolate x by
both sides of the inequality by 26. If you multiply
or divide both sides of an inequality by the same negative number, you must
the inequality symbol for the statement to be true.
Solve for x.
26x , 36
26x
36
 _____
 
 
 ​,  _____
  
 ​
x
26
Do you need to reverse the inequality sign?
B. Solve 2 , 24w. Then graph the solutions.
Isolate w by
Solve for w.
both sides of the inequality by 24.
2 , 24w
2
24w
 _____
   
 ​,  _____ 
 
 ​
___ ​
​ 21
 
2
Graph the solution.
A(n)
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w
–4 –3 –2 –1
0
1
2
3
4
5
Do you need to reverse the inequality sign?
circle should be used and the arrow should point to the
22
.
Holt McDougal Algebra 1
Name
lesson
Date
Class
Ready to Go On? Problem Solving Intervention
2-3 Solving One-Step Inequalities by Multiplying or Dividing
Solving one-step inequalities is much like solving one-step equations. To solve an
inequality that contains multiplication or division, undo the operation by dividing or
multiplying both sides of the inequality by the same number.
A piece of metal tubing is 90 inches long. Jamal needs to cut sections of tubing that are
12 inches long. What are the possible numbers of sections of tubing that Jamal can cut?
Understand the Problem
1. How much tubing does Jamal have?
2. How long does each section of tubing need to be?
3. What do you need to determine?
Make a Plan
4. What inequality symbol represents at most?
5. Let t represent the length of each section of tubing. Write an inequality for the situation.
The length
of tubing
12 inches
?
12
?
is at most
6. Solve the inequality by isolating t.
Solve
90 inches
90
12t # 90
90
12t
 ____
  
 ​#  ____  
 ​ t#
7. Does Jamal want to cut the tubing into partial sections?
8. Round
to get the greatest number of sections of tubing Jamal can cut.
9. Jamal can cut the tubing into at most
sections.
10. List the number of sections Jamal can cut.
sections
Look Back
11. Graph your solution on the number line. –1 0 1 2 3 4 5 6 7 8 9
12. Choose a number that is included in your solution.
13. Because each section is 12 inches long, multiply the number you chose in
Exercise 12 by 12. What is the result?
14. Is the result less than or equal to 90 inches?
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23
Does your solution make sense?
Holt McDougal Algebra 1
Name
Date
Class
Ready To Go On? Skills Intervention
Lesson
2-4
Solving Two-Step and Multi-Step Inequalities
Solving Two-Step Inequalities
Solve the inequality 8 $ 1 2 7r and graph the solutions.
8 $ 1 2 7r
2
–5 –4 –3 –2 –1
$ 2 7r
1
Isolate 27r by
7
7r
 __
   ​$  __   ​
0
2
3
4
5
2
1 from both sides.
What is the inverse of multiplication?
r
Do you need to reverse the sign?
To graph the solution, a(n)
circle should be used and the arrow should point to the
.
Solving Multi-Step Inequalities
Solve each inequality and graph the solutions.
A. 4(x 2 3) . 22
–5 –4 –3 –2 –1
0
4(x 2 3) . 22
4(x) 2 4(3) . 22
Distribute
4x 2
Simplify the left side.
___  ​ . ​ __ ​ 
​ 4x
4
. 22
4x .
x
Add
  
  
1  ​  ​
​  ​ __
6

2  ​  ​.
​  ​ __
3
1  ​  ​
​  ​ __
6
5x .
___  ​ . ​ __  ​
​ 5x
5
on the left side.
Graph the solution.
What is the LCD of the fractions?
4
Do you need to reverse the sign?
5  ​x 1 ​ __
2  ​  ​.
​  ​ __
6
3
5  ​x  ​1
​  ​ __
6
3
Divide both sides by 4.
 
2
to both sides of the equation.
5  ​x 1 ​ __
2  ​. ​ __
1  ​
B.​ __
6
3
6
1
Multiply both sides of the inequality by the LCD.
Distribute the LCD on the left side.
5x 1 4 . 1
x
 
Subtract
from both sides of the inequality.
Divide both sides by 5.
–2
–1
0
1
2
Do you need to reverse the sign?
Graph the solution.
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24
Holt McDougal Algebra 1
Name
Lesson
2-4
Date
Class
Ready to Go On? Problem Solving Intervention
Solving Two-Step and Multi-Step Inequalities
Inequalities that contain more than one operation require more than
one step to solve. Use inverse operations to undo the operations in the
inequality one at a time.
George has scored 21 points and 17 points in his first two basketball
games. How many points must he score in his third game to have an
average of at least 20 points per game?
Understand the Problem
1. How many games has George played?
2. How many combined points has George scored in the games?
3. How many more games will George play?
Make a Plan
4. What are you trying to determine?
5. How many total points must George score to average 20 points for 3 games?
6. What inequality symbol represents at least ?
7. Write an inequality to represent the situation where x equals the number of
1x
points in the third game.
60
Solve
8. Solve the inequality.
38 1 x $ 60
2
2
Subtract to isolate x.
x$
9. The number of points that George must score is at least
.
Look Back
10. Graph your solution on the number line.
18 19 20 21 22 23 24 25 26 27 28
11. Choose a number that is included in your solution.
12. Find the average of the number you chose in Exercise 11, and the values 21,
and 17. What is the result?
13. Is the result greater than or equal to 20?
14. Does your solution make sense?
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25
Holt McDougal Algebra 1
Name
Date
Class
Ready To Go On? Skills Intervention
Lesson
2-5
Solving Inequalities with Variables on Both Sides
Solving Inequalities with Variables on Both Sides
Solve x 2 10 $ 4x 2 16.
x 2 10 $ 4x 2 16
1
1
Isolate x by adding 10 to both sides.
x $ 4x 2
2
2
Simplify.
To isolate the constant term, subtract 4x from both sides.
x$
What is the inverse of multiplication?
Do you need to reverse the sign?
The solution is:
Simplifying Each Side Before Solving
Solve 4(3x 2 1) , 2(x 1 3).
4(3x 2 1) , 2(x 1 3)
(3x) 2
(1) ,
12x 2
,
x
2
x2
2
(3)
on the left side of the inequality.
Distribute
on the right side of the inequality.
1 6
Simplify both sides of the inequality.
x
Subtract 2x from both sides so that the coefficient
of x is positive.
,6
1
(x) 1
Distribute
1
x,
Add 4 to both sides of the equation.
Divide both sides of the equation by 10.
Do you need to reverse the sign?
The solution is:
All Real Numbers as Solutions or No Solutions
Solve 3y 1 4 . 3(y 1 3).
3y 1 4 . 3(y 1 3)
3y 1 4 . 3y 1
23y
.
Subtract 3y from both sides of the inequality.
23y
4.
To solve, the first step is to
Is the final answer true or false?
There are no values of x that make the inequality true. There are
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26
solutions.
Holt McDougal Algebra 1