Download Solve each inequality. Then graph it on a number line. 1. x − 8 > 4

Mid-Chapter Quiz
Solve each inequality. Then graph it on a number line.
x 8>4
The solution set is {x | x > 12}.
m
The solution set is {m | m
p
4}.
4< 7
The solution set is {p | p < 3}.
t
9
The solution set is {t | t
21}.
Lupe s allowance for the month is $60. She wants to go to a concert for which a ticket costs $45.
Write and solve an inequality that shows how much money she can spend that month after buying a concert
ticket.
She spends $9.99 on music downloads and $2 on lunch in the cafeteria. Write and solve an inequality that shows
how much she can spend after these purchases and the concert ticket.
a. Let m be the amount Lupe can spend after buying a concert ticket. Write an inequality. Because she can spend at
most $60, the inequality symbol is
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The solution set is {t | t
Mid-Chapter Quiz
21}.
Lupe s allowance for the month is $60. She wants to go to a concert for which a ticket costs $45.
Write and solve an inequality that shows how much money she can spend that month after buying a concert
ticket.
She spends $9.99 on music downloads and $2 on lunch in the cafeteria. Write and solve an inequality that shows
how much she can spend after these purchases and the concert ticket.
a. Let m be the amount Lupe can spend after buying a concert ticket. Write an inequality. Because she can spend at
most $60, the inequality symbol is
Lupe can spend $15 after buying a concert ticket.
b. Let m be the amount Lupe can spend after downloading music, buying lunch, and buying a concert ticket. Write an
inequality. Because she can spend at most $60, the inequality symbol is
Lupe can spend $3.01 after downloading music, buying lunch, and buying a concert ticket.
Define a variable, write an inequality, and solve each problem. Check your solution.
The sum of a number and 2 is no more than 6.
Sample answer: Let x = the number. The word sum means addition, and the phrase no more than means the
same as less than or equal to.
The solution set is {x | x
8}.
Check the endpoint with 8 and the direction with a value less than 8.
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Mid-Chapter Quiz
Lupe can spend $3.01 after downloading music, buying lunch, and buying a concert ticket.
Define a variable, write an inequality, and solve each problem. Check your solution.
The sum of a number and 2 is no more than 6.
Sample answer: Let x = the number. The word sum means addition, and the phrase no more than means the
same as less than or equal to.
The solution set is {x | x
8}.
Check the endpoint with 8 and the direction with a value less than 8.
A number decreased by 4 is more than 1.
Sample answer: Let x = the number. The phrase decreased by means subtraction, and the phrase more than
means greater than.
The solution set is {x | x > 3}.
Check the endpoint with 3 and the direction with a value greater than 3.
Twice a number increased by 3 is less than the number decreased by 4.
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Sample answer: Let x = the number. The word twice means to multiply by 2, and the phrase decreased by
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Mid-Chapter Quiz
Twice a number increased by 3 is less than the number decreased by 4.
Sample answer: Let x = the number. The word twice means to multiply by 2, and the phrase decreased by
means to subtract.
The solution set is {x | x < 7}.
Check the endpoint with -7 and the direction with a value less than -7.
Jane is saving money to buy a new cell phone that costs no more than $90. So far, she has
saved $52. How much more money does Jane need to save?
$38
more than $38
no more than $38
at least $38
Let c be the amount Jane still needs to save. Write an inequality. The phrase no more than means the same as less
than or equal to.
So, Jane needs to save no more than $38. The correct choice is choice C.
Solve each inequality. Check your solution.
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Mid-Chapter Quiz
So, Jane needs to save no more than $38. The correct choice is choice C.
Solve each inequality. Check your solution.
The solution set is {y | y 15}.
To check this answer, substitute a number greater than or equal to 15 into the original inequality. If y = 18, then
or 6
5, so the solution checks.
4<
The solution set is {c | c > 20}.
To check this answer, substitute a number greater than 20 into the original inequality. If c = 25, then
the solution checks.
8x > 24
The solution set is {x | x < 3}.
To check this answer, substitute a number less than 3 into the original inequality. If x = 4, then 8( 4) or 32 > 24,
so the solution checks.
2m
10
The solution set is {m | m
5}.
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To check
answer,
substitute
or 12
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a number less than or equal to 5 into the original inequality. If m = 6, then 2( 6)
10, so the solution checks.
The solution set is {x | x < 3}.
To check this
answer, substitute a number less than 3 into the original inequality. If x = 4, then 8( 4) or 32 > 24,
Mid-Chapter
Quiz
so the solution checks.
2m
10
The solution set is {m | m
5}.
To check this answer, substitute a number less than or equal to 5 into the original inequality. If m = 6, then 2( 6)
or 12
10, so the solution checks.
<
The solution set is
.
To check this answer, substitute a number less than
x = 1, then
, so the
solution checks.
9a
45
The solution set is {a | a 5}.
To check this answer, substitute a number less than or equal to 5 into the original inequality. If a = 2, then 9(2) or
18
45, so the solution checks.
> 3
The Manual
solution
set is {w
| w > 18}.
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To check this answer, substitute a number greater than 18 into the original inequality. If w = 12, then
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2>
The solution set is {a | a 5}.
To check this
answer, substitute a number less than or equal to 5 into the original inequality. If a = 2, then 9(2) or
Mid-Chapter
Quiz
18
45, so the solution checks.
> 3
The solution set is {w | w > 18}.
To check this answer, substitute a number greater than 18 into the original inequality. If w = 12, then
2>
3, so the solution checks.
< 2
The solution set is {k | k < 14}.
To check this answer, substitute a number less than 14 into the original inequality. If k = 21, then
3 < 2,
so the solution checks.
The world s heaviest flying bird is the great bustard. A male bustard can be up to 4 feet long and weigh
up to 40 pounds.
Write inequalities to describe the ranges of lengths and weights of male bustards.
Male bustards are usually about four times as heavy as females. Write and solve an inequality that describes the
range of weights of female bustards.
a. Let
w be the weight of a male bustard. The phrase up to means the
same as less than. Both the length and weight of a bustard must be more than zero.
0< <4
0 < w < 40
b. Let w be the weight of a female bustard. The weight of a male bustard can be represented by 4w.
Bill is building a fence around a square garden to keep deer out. He has 60 feet of fencing. Find the
garden.
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maximum
ofbya Cognero
side of the
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Mid-Chapter Quiz
Bill is building a fence around a square garden to keep deer out. He has 60 feet of fencing. Find the
maximum length of a side of the garden.
Let x be the side length of Bill s square garden. The perimeter of the garden can be represented by 4x. Because Bill
has only 60 feet of fencing, the perimeter must be less than or equal to 60 feet.
So, the garden can be at most 15 feet on each side.
Solve each inequality. Check your solution.
4a 2 > 14
The solution set is {a | a > 4}.
To check this answer, substitute a number greater than 4 into the original inequality. Let a = 5.
So, the solution checks.
2x
x
10
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Mid-Chapter
Quiz checks.
So, the solution
2x
x
10
The solution set is {x | x 7}.
To check this answer, substitute a number greater than or equal to 7 into the original inequality. Let x = 10.
So, the solution checks.
p +4< 9
The solution set is {p | p > 13}.
To check this answer, substitute a number greater than 13 into the original inequality. Let p = 15.
So, the solution checks.
3
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Mid-Chapter Quiz
So, the solution checks.
3
The solution set is {d | d
16}.
To check this answer, substitute a number greater than or equal to 16 into the original inequality. Let d = 12.
So, the solution checks.
2(4b + 1) < 3b + 8
The solution set is {b | b > 2}.
To check this answer, substitute a number greater than 2 into the original inequality. Let b = 0.
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So, the solution checks.
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Mid-Chapter Quiz
So, the solution checks.
2(4b + 1) < 3b + 8
The solution set is {b | b > 2}.
To check this answer, substitute a number greater than 2 into the original inequality. Let b = 0.
So, the solution checks.
Define a variable, write an inequality, and solve each problem. Check your solution.
Three times a number increased by 8 is no more than the number decreased by 4.
Sample answer: Let x = the number. Times means multiplication, increased by means addition, no more than
means less than or equal to, and decreased by means subtraction.
The solution set is {x | x
6}.
To check this answer, substitute a number less than or equal to 6 into the original inequality. Let x = 7.
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So, the solution checks.
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Mid-Chapter Quiz
So, the solution checks.
Define a variable, write an inequality, and solve each problem. Check your solution.
Three times a number increased by 8 is no more than the number decreased by 4.
Sample answer: Let x = the number. Times means multiplication, increased by means addition, no more than
means less than or equal to, and decreased by means subtraction.
The solution set is {x | x
6}.
To check this answer, substitute a number less than or equal to 6 into the original inequality. Let x = 7.
So, the solution checks.
Two thirds of a number plus 5 is greater than 17.
Sample answer: Let x = the number. Of means multiplication.
The solution set is {x | x > 18}.
To check this answer, substitute a number greater than 18 into the original inequality. Let x = 21.
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Mid-Chapter
Quiz checks.
So, the solution
Two thirds of a number plus 5 is greater than 17.
Sample answer: Let x = the number. Of means multiplication.
The solution set is {x | x > 18}.
To check this answer, substitute a number greater than 18 into the original inequality. Let x = 21.
So, the solution checks.
Shoe rental costs $2, and each game bowled costs $3. How many games can Kyle bowl
without spending more than $15?
2
3
4
5
Let g be the number of games Kyle bowls.
The solution set is
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.
Because Kyle cannot bowl one-third of a game, the most games he can bowl is 4. So, the correct choice is H.
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Mid-Chapter Quiz
So, the solution checks.
Shoe rental costs $2, and each game bowled costs $3. How many games can Kyle bowl
without spending more than $15?
2
3
4
5
Let g be the number of games Kyle bowls.
The solution set is
.
Because Kyle cannot bowl one-third of a game, the most games he can bowl is 4. So, the correct choice is H.
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