Equations and Inequalities
Review
Ann uses the distributive property to write an
expression equivalent to 4x + 16. Which of the
following best represents Ann’s expression?
A.4(x + 6)
B.2(2x + 6)
C.4(x + 16)
D.4(x+4)
ANSWER
Ann uses the distributive property to write an
expression equivalent to 4x + 16. Which of the
following best represents Ann’s expression?
A.4(x + 6)
B.2(2x + 6)
C.4(x + 16)
D.4(x+4)
Amy charges $11 per hour for her pet sitting services. She pet sits to earn money for
her class trip. She needs to earn at least $165 for the trip. The inequality 11x ≥ 165
can be used to determine the number of hours, x, Aiko needs to babysit to reach her
goal. Which number line best represents the solution to the inequality?
ANSWER
Amy charges $11 per hour for her pet sitting services. She pet sits to earn money for
her class trip. She needs to earn at least $165 for the trip. The inequality 11x ≥ 165
can be used to determine the number of hours, x, Aiko needs to babysit to reach her
goal. Which number line best represents the solution to the inequality?
11x ≥ 165
11
11
x ≥ 15
Write an inequality for the statement below.
Missy had a collection of 278 seashells. On her trip to the
beach, she found more seashells. Missy now has over 500
seashells in her collection. Find z, the number of seashells
Missy found at the beach.
ANSWER
The regular price for a game system was at most $500.
It was on sale this week for $278. Find z, the amount of
money saved by purchasing the game system on sale.
278 + x ≤ 500
If x = -5, would the equation be true?
-10 + x = -15
ANSWER
If x = -5, would the equation be true?
-10 + x = -15
Yes
If x = -5, would the equation be true?
-7x = -21
ANSWER
If x = -5, would the equation be true?
-7x = -21
No
If x = -5, would the inequality be true?
-24 > 15x
ANSWER
If x = -5, would the inequality be true?
-24 > 15x
-24 > -75 True
If x = -5, would the equation be true?
x - 5 ≥ -9
ANSWER
If x = -5, would the equation be true?
x - 5 ≥ -9
-10 ≥ -9 No
The equation 4w = 16 is modeled below.
What value of w makes this equation true?
ANSWER
The equation 4w = 16 is modeled below.
What value of w makes this equation true?
Perform the opposite operation. 16 ÷ 4 = 4 so w = 4
Kelvin modeled an expression using the algebra tiles shown.
Which of the following could not be the expression Kelvin modeled?
A.
B.
C.
D.
5(x + 1)
2 + 2 + 3x + 2x + 1
2x + 2x + 3 + 2 + 2x
2(x + 2) + 3x + 1
Kelvin modeled an expression using the algebra tiles shown.
Which of the following could not be the expression Kelvin modeled?
A.
B.
C.
D.
5(x + 1)
2 + 2 + 3x + 2x + 1
2x + 2x + 3 + 2 + 2x
2(x + 2) + 3x + 1
Max uses a balance scale to solve an equation, as shown below.
Which value of x best represents the solution to the equation?
A. x = -14
B. x = 2
C. x = -2
D. x = 14
ANSWER
Max uses a balance scale to solve an equation, as shown below.
Which value of x best represents the solution to the equation?
A. x = -14
B. x = 2
C. x = -2
D. x = 14
During Jeremy’s basketball game, he scored 16 points for his team. The
rest of his teammates scored a total of y points. If the team won the
game with 88 points, which equation could be used to determine the
points earned by Jeremy’s teammates?
A. 16 + y = 88
B.
16
=
88
y
C. 16y = 88
D. y – 16 = 88
ANSWER
During Jeremy’s basketball game, he scored 16 points for his team. The
rest of his teammates scored a total of y points. If the team won the
game with 88 points, which equation could be used to determine the
points earned by Jeremy’s teammates?
A. 16 + y = 88
B.
16
=
88
y
C. 16y = 88
D. y – 16 = 88
Which of these can be written as an equation?
A.
B.
C.
D.
Three times 0.845 plus m
Three more than twice a number is 13
One third the product of nine and j
Five times a number and 4
ANSWER
Which of these can be written as an equation?
A. Three times 0.845 plus m 3 0.845 + m
B. Three more than twice a number is 13 3 + 2n = 13
C. One third the product of nine and j
D. Five times a number and 4 5(n + 4)
9𝑗
3
Which expression is equivalent to 4(x + 5)
A.4x + 5
B.4 + x + 5
C.4x + 20
D.4x + 9
ANSWER
Which expression is equivalent to 4(x + 5)
A.4x + 5
B.4 + x + 5
C.4x + 20
D.4x + 9
In the expression shown p represents a rational number.
7p
What value of p makes the expression equal a number less than 7?
A.
B.
C.
D.
4
4
9
5
3
4
5
4
ANSWER
In the expression shown p represents a rational number.
7p
What value of p makes the expression equal a number less than 7?
A.
B.
C.
D.
4
4
9
5
3
4
5
4
Cindy carries books and supplies in her backpack that weigh 8 total
pounds. Her backpack weighs x pounds. Which equation can be
used to find t, the total weight of both the contents of her backpack
and backpack?
A. t = 8x
B. t = 8 + x
C. t = 8 – x
D. t =
8
𝑥
ANSWER
Cindy carries books and supplies in her backpack that weigh 8 total
pounds. Her backpack weighs x pounds. Which equation can be
used to find t, the total weight of both the contents of her backpack
and backpack?
A. t = 8x
B. t = 8 + x
C. t = 8 – x
D. t =
8
𝑥
What is the value of k in the inequality sentence shown
below?
𝑘
4
≤ 11
ANSWER
What is the value of k in the inequality sentence shown
below?
𝑘
4
≤ 11
k ≤ 44
Nick wants to spend no more than $20 at the book store. He already
picked out a book for $5. The inequality x + 5 ≤ 20 can be used to
determine the number of additional items, x, he can purchase at the
book store. Which number line best represents the solution to the
inequality?
ANSWER
Nick wants to spend no more than $20 at the book store. He already
picked out a book for $5. The inequality x + 5 ≤ 20 can be used to
determine the number of additional items, x, he can purchase at the
book store. Which number line best represents the solution to the
inequality?
Which expression is equivalent to (4d + 10) + 5?
A.
B.
C.
D.
5 + 4d – 10
4(d + 6) + 5
4d + 10 + d
4d + 15
ANSWER
Which expression is
equivalent to (4d + 10) + 5?
A. 5 + 4d – 10
B. 4(d + 6) + 5
C. 4d + 10 + d
D. 4d + 15
Mrs. Augenstein wrote the following phrase down on the board.
21 less than a number is 52
Which of the following matches the phrase that Mrs. Augenstein wrote?
A. 21 – n = 52
B. n – 21 = 52
C. 52 – 21 = n
D. 21 + n = 52
ANSWER
Mrs. Augenstein wrote the following phrase down on the board.
21 less than a number is 52
Which of the following matches the phrase that Mrs. Augenstein wrote?
A. 21 – n = 52
B. n – 21 = 52
C. 52 – 21 = n
D. 21 + n = 52
The model represents an inequality statement.
Solve the inequality and graph the solution set
on the number line shown below.
ANSWER
The model represents an inequality statement.
Solve the inequality and graph the solution set
on the number line shown below.
3x > -21
x > -7