math assignment
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©CurriculumAssociates, LLC Copying is not permitted. 215Lesson 20
Solve Inequalities
Name: Solve Inequalities
Lesson 20
Prerequisite: Solve Equations
Study the example problem showing how to solve an
equation. Then solve problems 1–7.
1 What does b represent in the bar model?
2 What does each part of the bar model represent?
3 Explain how the model shows that 7b 5 91
4 What operation will you use to solve the equation
7b 5 91? Solve the equation to find the number of bulbs,
and justify each step you take to solve the equation
Show your work.
Solution:
Example
Taryn planted 91 tulip bulbs in 7 rows She planted the
same number of bulbs in each row How many bulbs
did she plant in each row?
Create a bar model to represent the 7 rows and the total
number of bulbs that Taryn planted
91
bb b b b b b
©Curriculum Associates, LLC Copying is not permitted.216 Lesson 20 Solve Inequalities
Solve.
5 Milo and Audrey sold tickets to the school concert
Milo sold 14 fewer tickets than Audrey If Milo sold
32 tickets, how many tickets did Audrey sell?
Show your work.
Solution:
6 Carmen buys 4 daisies and some roses to make a
flower arrangement The number of daisies is 1 ·· 3 of the
number of roses that she buys How many roses does
she buy?
Show your work.
Solution:
7 Write a multiplication equation and a subtraction
equation that both involve a fraction and have the
same solution Solve your equations to show that
the solutions are the same
©Curriculum Associates, LLC Copying is not permitted. 217Lesson 20 Solve Inequalities
Name:
Lesson 20
Write and Solve an Inequality
Study the example problem showing how to write and solve an
inequality for a real-world problem. Then solve problems 1–9.
1 Why is the graph in the example shaded to the left?
2 Is 2$10 a solution? Substitute 210 into the inequality
in the example to check
3 Name an amount that is NOT a solution to the
inequality Explain how you know
4 Suppose the bank sent Mr Gomez a notice whenever
the amount in his account dropped to $15 or less How
would the graph in the example change?
Example
Mr Gomez gets a notice from the bank when the amount
in his checking account drops below $20 For what
amounts will Mr Gomez receive a notice from the bank?
Use words and symbols to represent the situation Let x
represent the amount in Mr Gomez’s account When x is
less than $20, the bank will send a notice
x , 20
Graph the inequality to show all of the solutions Use an
open circle shows that 20 is NOT a solution
025210215220225 5 10 15 20 25
Vocabulary
inequality a statement
that contains the symbol
,, ., #, or $ For any
inequality, there are
many possible solutions
These are inequalities
x , 5
x . 22
x # 15
x $ 0
©Curriculum Associates, LLC Copying is not permitted.218 Lesson 20 Solve Inequalities
Solve.
5 Write the inequality shown on each graph
a.
222324 21 0 1
b.
210 10 20 30 40230 220250 240 0 50
6 The children at Lincoln School go outside for
recess if the temperature is 3°C or higher For
what temperatures will the students go
outside? Write an inequality to represent this
situation Then graph the solution
7 If your score on a computer game is less than 0, you
lose your next turn For what scores will you lose your
turn? Write an inequality to represent this situation
Then graph the solution
8 Write a real-world situation for this inequality: x $ 9
9 Explain how an equation and an inequality are
different Give an example of each
2 4 5 6 70 122 21 3 8
24 0 2 4 628 26212 210 22 8
©Curriculum Associates, LLC Copying is not permitted. 219Lesson 20 Solve Inequalities
Name:
Lesson 20
More Inequalities
Study the example problem showing how to write and
solve an inequality. Then solve problems 1–9.
1 Leigh is 40 inches tall Can she ride on the roller coaster?
2 Brennon is 38 inches tall Can he ride on the roller
coaster? Use the graph to explain your answer
3 Joy wrote the inequality 40 # x to represent the
situation Is her inequality correct?
4 Suppose this graph represents a problem about the
height of people riding the roller coaster How would
the situation have changed?
10 30 40 50 60210 0230 220 20 70
Example
You need to be at least 40 inches tall to ride on the roller
coaster at the amusement park What are some possible
heights for riders? Write an inequality to represent the
heights, and graph the solution on a number line
Use symbols to represent the situation Let x be the
possible heights in inches for riders
x $ 40
Graph the inequality to show all of the solutions
10 30 40 50 60210 0230 220 20 70
©Curriculum Associates, LLC Copying is not permitted.220 Lesson 20 Solve Inequalities
Solve.
Use this situation for problems 5–6.
You must spend at least $10 at the grocery store to get a
free greeting card
5 Write an inequality to represent the amount you need
to spend to get a free greeting card Then graph the
solution on the number line
6 If you spend $9 50, will you get a free greeting card?
Use the graph to explain how you know
7 Zarina is scuba diving She will not dive below
230 meters relative to the surface of the water Write
an inequality that represents this situation Is 220 a
solution to the inequality? Explain how you know
8 Write an inequality that has the solution shown
on the graph Then write a real-world situation for
the inequality
5 7 8 9 103 41 2 6 11
9 Markim looks at the graph below and says that 21 is
the only possible negative solution Do you agree or
disagree? Explain
0 2 3 4 522 2124 23 1 6
12 16 18 20 228 104 6 14 24
©Curriculum Associates, LLC Copying is not permitted. 221Lesson 20 Solve Inequalities
Name:
Lesson 20
Solve Inequalities
Solve the problems.
3 The graph shows information about the low
temperature in a particular city in degrees Celsius each
day during one week in January Write an inequality
for this situation Then write in words what the graph
shows about the temperature readings
26 24 22 0 6 8 1028210 2 4
2 Samuel wants to eat at least 15 grams of protein each
day Let x represent the amount of protein he should
eat each day to meet his goal Which inequality
represents this situation?
A x , 15 C x # 15
B x . 15 D x $ 15
Karli chose B as the correct answer How did she get
that answer?
1 Write an inequality for each graph
a.
b.
21 0 12223 2
What does the
direction of the
arrow on the shaded
line tell you about
the inequality?
Would a graph for
this situation have
an open circle or a
closed circle?
What are some
words that describe
a situation in which
the shaded line on
the graph points
left?
10 30 40 50 60210 0230 220 20 70
©Curriculum Associates, LLC Copying is not permitted.222 Lesson 20 Solve Inequalities
6 Consider the inequality x . 20 75 Tell whether each
statement is True or False
a. 20 75 is a solution to
the inequality u True u False
b. There are many solutions
to this inequality u True u False
c. All of the solutions to the
inequality are negative u True u False
d. The inequality 20 75 , x
is equivalent to the given
inequality u True u False
e. 24 5 is a solution to the
inequality u True u False
Solve.
4 Kalista practices the piano for at least 8 hours each
week Write an inequality for this situation Then graph
the solution on the number line
5 Which of these values is a solution
to the inequality x 2 1 $ 6?
7 3 1 ·· 2 2 5 10
Show your work.
Solution:
Does a given value
for x make the
inequality true or
false?
How do you know
whether a given
value is a solution to
the inequality?
Does “at least”
include 8 as a
solution?
2 4 6 8 14 16 18022 10 12