Algebra 1 AVENTA07-Alg1Block and Alg1Sem1
UNIT 5 Inequalities Quiz and Test Multiple Choice Feedback.
5-Quiz
Question: The solution for a + 4 < 9 is shown on the number line below.
1 #1
Answer: True
Correct Feedback: The solution is a < 5. The solution does not include 5,
denoted by the open circle on 5. The solution is all numbers less than 5,
denoted by the red line running left of 5.
Incorrect Feedback: The solution is a < 5. The solution does not include 5,
denoted by the open circle on 5. The solution is all numbers less than 5,
denoted by the red line running left of 5.
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1 #2
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1 #3
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1 #4
Question: Which of the following represents the solution of 17 + x > -2 in set
notation?
Answer: {x| x > -19}
Correct Feedback: To solve, subtract 17: x > -19.
Incorrect Feedback: To solve, subtract 17: x > -19.
Question: Which inequality has the solution shown on the number line?
Answer:
Correct Feedback: The solution is x ≥ -2. The solution is = -2, denoted by
the red dot on -2, and all numbers greater than -2, denoted by the red line to
the right of -2.
Incorrect Feedback: The solution is x ≥ -2. The solution is = -2, denoted by
the red dot on -2, and all numbers greater than -2, denoted by the red line to
the right of -2.
Question: Which inequality best represents the sentence? A number
decreased by 8 is at most 15.
Answer:
Correct Feedback: To say that the number is at most 15, means that it
cannot be greater than 15. Therefore, it must be less than or equal to 15.
Incorrect Feedback: To say that the number is at most 15, means that it
cannot be greater than 15. Therefore, it must be less than or equal to 15.
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1 #6
Question:
Answer:
Correct Feedback: Add 19.
Incorrect Feedback: Add 19.
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1 #9
Question:
Answer:
Correct Feedback: Multiply by 4.
Incorrect Feedback: Multiply by 4.
Question: Solve -8x < 64.
Answer: x > -8
Correct Feedback: Divide by -8 and reverse the symbol.
Incorrect Feedback: Divide by -8 and reverse the symbol.
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2 #3
Question:
Answer: x ≤ 6
Correct Feedback: Multiply by 3/2. (3/2)(-4) = -12/2 = -6.
Incorrect Feedback: Multiply by 3/2. (3/2)(-4) = -12/2 = -6.
Question: Solve the following problem: Parking in the city lot can have no
more than 25% of the spaces limited to compact cars. What is the number of
total spaces in the lot if there are 30 spaces allocated to compact cars?
Answer: 120
Correct Feedback: 0.25x ≤ 30. Divide by 0.25: x ≤ 120.
Incorrect Feedback: 0.25x ≤ 30. Divide by 0.25: x ≤ 120.
Question: Is 0 a solution of -2 < x < 5?
Answer: yes
Correct Feedback: The solution includes any number that is between -2 and
5.
Incorrect Feedback: The solution includes any number that is between -2
and 5.
Question: Is 8 a solution of x < -1 or x > 7?
Answer: yes
Correct Feedback: A solution will be either less than -1 or greater than 7.
Since 8 is greater than 7, it is a solution.
Incorrect Feedback: A solution will be either less than -1 or greater than 7.
Since 8 is greater than 7, it is a solution.
Question: Which of the following is the solution for the inequality, -5 < x - 4 <
0?
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2 #4
Answer:
Correct Feedback: To solve, add 4 to each part: -1 < x < 4. The solution will
be all numbers between -1 and 4, denoted by the red line.
Incorrect Feedback: To solve, add 4 to each part: -1 < x < 4. The solution
will be all numbers between -1 and 4, denoted by the red line.
Question: Which of the following is the solution for x - 2 < 3 and x + 2 > -2?
Answer:
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2 #1
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2 #2
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2 #5
Correct Feedback: Solve each equation. The solution is x < 5 and x > -4.
The numbers that are both less than 5 and greater than -4 are between -4
and 5. So, the solution in final form is -4 < x < 5.
Incorrect Feedback: Solve each equation. The solution is x < 5 and x > -4.
The numbers that are both less than 5 and greater than -4 are between -4
and 5. So, the solution in final form is -4 < x < 5.
Question: Which of the following is a solution for 2b + 5 < -1 or b - 4 > -4?
Answer: b < -3 or b > 0
Correct Feedback:
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2 #8
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2 #9
Incorrect Feedback:
Question: Which of the following is a solution for 4m - 5 > -9 or 4m - 5 < 3?
Answer: All Real Numbers
Correct Feedback: When each inequality is solved, we have m > -1 or m < 2.
Since any number is either greater than -1 or less 2, the solution is all real
numbers.
Incorrect Feedback: When each inequality is solved, we have m > -1 or m <
2. Since any number is either greater than -1 or less 2, the solution is all real
numbers.
Question: Which of the following is the solution of a - 4 > 1 and a + 2 < 1?
Answer: no solution
Correct Feedback: When each inequality is solved, we have a > 5 and a < 1. Since no number is both greater than 5 and less than -1, we have no
solution.
Incorrect Feedback: When each inequality is solved, we have a > 5 and a <
-1. Since no number is both greater than 5 and less than -1, we have no
solution.
Question: Solve 2x - 3 < 5.
Answer: x < 4
Correct Feedback: Add 3: 2x < 8. Divide by 2: x < 4.
Incorrect Feedback: Add 3: 2x < 8. Divide by 2: x < 4.
Question: Solve -2x - 3 < 11.
Answer: x > -7
Correct Feedback: Add 3: -2x < 14. Divide by -2 and reverse the symbol: x
> -7.
Incorrect Feedback: Add 3: -2x < 14. Divide by -2 and reverse the symbol:
x > -7.
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2 #10
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3 #2
Question: Solve x/4 + 12 < 42.
Answer: x < 120
Correct Feedback: Subtract 12: x/4 < 30. Multiply by 4: x < 120.
Incorrect Feedback: Subtract 12: x/4 < 30. Multiply by 4: x < 120.
Question: Match each absolute value sentence with its solution set.
Answer:
Correct Feedback:
Incorrect Feedback:
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4 #2
Question: Which of the following is the inequality 2x + 4y < 8 when solved
for y?
Answer: y < 2 – ½ x
Correct Feedback:
Incorrect Feedback:
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4#3
Question: Mark all ordered pairs which ARE a solution for y < 3 - 2x.
Answer: (-1, 3) and (-4, 5)
Correct Feedback:
Incorrect Feedback:
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Question: Which point is NOT a solution of
Answer: (4,4)
Correct Feedback: Is 4 + 2(4) ≤ 8? 4 + 8 = 12 which is not less than or
equal to 8.
Incorrect Feedback: Is 4 + 2(4) ≤ 8? 4 + 8 = 12 which is not less than or
equal to 8.
Question: The boundary line for the inequality y > 2x + 4 has a slope of 4.
Answer: False
Correct Feedback: The slope is 2.
Incorrect Feedback: The slope is 2.
Question: Which point is NOT a solution of y < -3?
Answer: (3,0)
Correct Feedback: Substituting the y value of (3, 0), 0 < -3, which is false.
Incorrect Feedback: Substituting the y value of (3, 0), 0 < -3, which is false.
Question: The number 5 is one of the solutions for the inequality 3x < 21.
Answer: True
Correct Feedback: The solution is x < 7. Since 5 is less than 7, it is a
solution.
Incorrect Feedback: The solution is x < 7. Since 5 is less than 7, it is a
solution.
Question: Solve x - 8 > -2.
Answer: x > 6
Correct Feedback: Add 8.
Incorrect Feedback: Add 8.
Question: Mark the inequality which is represented by this graph.
Answer: x < 5
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Correct Feedback: The red line indicates all numbers less than 5.
Incorrect Feedback: The red line indicates all numbers less than 5.
Question: Solve -4x > 12.
Answer: x < -3
Correct Feedback: Divide by -4 and reverse the symbol.
Incorrect Feedback: Divide by -4 and reverse the symbol.
Question: Solve the inequality, -3x - 2 < 5.
Answer: x > -7/3
Correct Feedback: Add 2: -3x < 7. Divide by -3 and reverse the symbol: x
> -7/3.
Incorrect Feedback: Add 2: -3x < 7. Divide by -3 and reverse the symbol: x
> -7/3.
Question: Which of the following is a solution of the compound inequality -1
< 2n + 1 < 5?
Answer: -1 < n < 2
Correct Feedback: Subtract 1: -2 < 2n < 4. Divide by 2: -1 < n < 2.
Incorrect Feedback: Subtract 1: -2 < 2n < 4. Divide by 2: -1 < n < 2.
Question: Which of the following is a solution of the compound inequality?
3x + 8 < 2 or x + 12 > 2 - x
Answer: All real numbers
Correct Feedback: Solve each inequality: x < -2 or x > -5. Since any
number is either less than -2 or greater than -5, the solution is all real
numbers.
Incorrect Feedback: Solve each inequality: x < -2 or x > -5. Since any
number is either less than -2 or greater than -5, the solution is all real
numbers.
Question: Solve |x + 6| = 12.
Answer: {6, -18}
Correct Feedback:
Incorrect Feedback:
Question: Solve |2x -5| > 7.
Answer: x > 6 or x < -1
Correct Feedback:
Incorrect Feedback:
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Question: Evaluate
Answer: 50
Correct Feedback: =5(4+6) = 5(10) = 50.
Incorrect Feedback: =5(4+6) = 5(10) = 50.
Question: Which of the following ordered pairs is a solution of y < 2x -6?
Answer: (2, -3)
Correct Feedback: Substituting (2, -3): -3 < 2(2) – 6. -3 < 4 – 6. -3 < -2.
True.
Incorrect Feedback: Substituting (2, -3): -3 < 2(2) – 6. -3 < 4 – 6. -3 < -2.
True.
Question: Solve 4x + 3y = 8x + y for y.
Answer: y = 2x
Correct Feedback:
Incorrect Feedback:
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Answer: 4
Correct Feedback: h(-3)=(-3)2 – 5 = 9 – 5 = 4.
Incorrect Feedback: h(-3)=(-3)2 – 5 = 9 – 5 = 4.
Question:
Answer: 41
Correct Feedback: =15 · 3 – 4 = 45 – 4 = 41.
Incorrect Feedback: =15 · 3 – 4 = 45 – 4 = 41.
Question: Simplify 3(m + 6n) + 2(4m + 3n).
Answer: 11m + 24n
Correct Feedback: Distribute: 3m + 18n + 8m + 6n = (3m + 8m) + (18n +
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6n) = 11m + 24n.
Incorrect Feedback: Distribute: 3m + 18n + 8m + 6n = (3m + 8m) + (18n +
6n) = 11m + 24n.
Question: Determine the x-intercept and y-intercept of 3x - 6y = 12.
Answer: (4, 0) and (0, -2)
Correct Feedback:
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Incorrect Feedback:
Question: Does the data in this table represent linear data?
x
1
2
3
4
y
6
12
24
48
Answer: no
Correct Feedback: For the first 4 points, the difference in x is 1. However
the difference in y is 6, 12, and 24.
Incorrect Feedback: For the first 4 points, the difference in x is 1. However
the difference in y is 6, 12, and 24.
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#22
Question: Find the 6th term in the sequence:
Answer: 32
Correct Feedback: t6 = 5(6) + 2 = 30 + 2 = 32.
Incorrect Feedback: t6 = 5(6) + 2 = 30 + 2 = 32.
Question:
Answer:
Correct Feedback: = 24 m2(4) n(-3)(4) = 16m8n-12.
Incorrect Feedback: = 24 m2(4) n(-3)(4) = 16m8n-12.
Question:
Answer:
Correct Feedback:
Incorrect Feedback:
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Question: Write an equation in slope-intercept form of the line that passes
through (4, 8) and (0, -2).
Answer: y = 5/2 x - 2
Correct Feedback: Slope = (-2 – 8)/(0 – 4) = -10/-4 = 5/2. The y-intercept is
(0, -2). So, y = mx + b = 5/2 x – 2.
Incorrect Feedback: Slope = (-2 – 8)/(0 – 4) = -10/-4 = 5/2. The y-intercept
is (0, -2). So, y = mx + b = 5/2 x – 2.
Question: The slope of the line perpendicular to y = 3/4 x - 7 is
Answer: -4/3
Correct Feedback: This line’s slope is ¾. The perpendicular line’s slope is
the opposite reciprocal of -4/3.
Incorrect Feedback: This line’s slope is ¾. The perpendicular line’s slope is
the opposite reciprocal of -4/3.
Question: The equation in point-slope form of the line which passes through
(-2, 3) and is parallel to 3x + 2y = 10 is
Answer: y - 3 = -3/2 (x + 2)
Correct Feedback: When solved for y, the equation is y = -3/2 x + 5. The
parallel line will also have a slope of -3/2. Using (-2, 3) for the point, the
equation is y – 3 = -3/2 (x + 2).
Incorrect Feedback: When solved for y, the equation is y = -3/2 x + 5. The
parallel line will also have a slope of -3/2. Using (-2, 3) for the point, the
equation is y – 3 = -3/2 (x + 2).
Question: Solve 6(x + 1) - 4 = 3x + 2.
Answer: 0
Correct Feedback: Distribute: 6x + 6 – 4 = 3x + 2. Simplify: 6x + 2 = 3x +
2. Subtract 3x: 3x + 2 = 2. Subtract 2: 3x = 0. Divide by 3: x = 0.
Incorrect Feedback: Distribute: 6x + 6 – 4 = 3x + 2. Simplify: 6x + 2 = 3x +
2. Subtract 3x: 3x + 2 = 2. Subtract 2: 3x = 0. Divide by 3: x = 0.
Question: Determine the slope of the line which passes through these two
points: (-1, 3) and (6, 9).
Answer: 6/7
Correct Feedback: m = (9 – 3)/(6 - -1) = 6/7.
Incorrect Feedback: m = (9 – 3)/(6 - -1) = 6/7.
Question: If y varies directly as x and y = 14 when x = 8, find x when y = 21.
Answer: 12
Correct Feedback: y = kx. 14 = k(8). k = 14/8 = 1.75. y = 1.75x. 21 =
1.75x. So, x = 21/1.75 = 12.
Incorrect Feedback: y = kx. 14 = k(8). k = 14/8 = 1.75. y = 1.75x. 21 =
1.75x. So, x = 21/1.75 = 12.
Question: Solve 2(2m + 3) - 8 > 4m + 2.
Answer: no solution
Correct Feedback: Distribute: 4m + 6 - 8 > 4m + 2. Simplify: 4m – 2 > 4m
+ 2. Subtract 4m: -2 > 2. This is false and there is no solution.
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Incorrect Feedback: Distribute: 4m + 6 - 8 > 4m + 2. Simplify: 4m – 2 > 4m
+ 2. Subtract 4m: -2 > 2. This is false and there is no solution.
Question: Which graph is a solution of |2x - 3| < 5 ?
Answer:
Correct Feedback:
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Incorrect Feedback:
Question: What is the range of y = 5x -2 if the domain is {-3, -1, 0, 1, 3}?
Answer: {-17, -7, -2, 3, 13}
Correct Feedback: When each of {-3, -1, 0, 1, 3} are substituted as the x
value in the equation, the y-values are {-17, -7, -2, 3, 13}.
Incorrect Feedback: When each of {-3, -1, 0, 1, 3} are substituted as the x
value in the equation, the y-values are {-17, -7, -2, 3, 13}.
Question: What is the solution set for the inequality 3x - 7 >9 if the
replacement set is {-2, 0, 5, 7, 11, 13}?
Answer: {7, 11, 13}
Correct Feedback: When each member of the replacement set is substituted
for x in the inequality, we only get true statements for {7, 11, 13}.
Incorrect Feedback: When each member of the replacement set is
substituted for x in the inequality, we only get true statements for {7, 11, 13}.
Question:
Round your answer to the nearest tenth.
Answer: 2.4
Correct Feedback:
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Incorrect Feedback:
Question: Is the following relation a function?
{(0, 5), (3, 8), (5, 9), (7, 9)}
Answer: yes
Correct Feedback: Each x-value is paired with one and only one y-value.
Incorrect Feedback: Each x-value is paired with one and only one y-value.
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Question: Which are counterexamples of the following statement?
If the sum of x and y is negative, then both x and y are negative.
Answer: “ x = -10 and y = 5 “ and “x = -6 and y = 0”
Correct Feedback: -10 + 5 = -5 and -6 + 0 = -6. Their sums are negative,
but x and y are not both negative.
Incorrect Feedback: -10 + 5 = -5 and -6 + 0 = -6. Their sums are negative,
but x and y are not both negative.
Question: Which is the least number of the following? 4/5, 0.89, 13/15
Answer: 4/5
Correct Feedback: 4/5, 0.89, 13/15, written as decimals to the hundredths
place are: 0.80, 0.89, 0.86… Comparing the three, we see that 0.80 or 4/5 is
the least.
Incorrect Feedback: 4/5, 0.89, 13/15, written as decimals to the hundredths
place are: 0.80, 0.89, 0.86… Comparing the three, we see that 0.80 or 4/5 is
the least.
Question: If a coat that originally cost $115 was marked down 20%, how
much would be marked off the price?
Answer: 23
Correct Feedback: 20% of 115 = 0.20(115) = 23.
Incorrect Feedback: 20% of 115 = 0.20(115) = 23.
Question: If a shirt costs $39 and the sales tax is 5%, how much is the total
cost of buying the shirt?
Answer: $40.95
Correct Feedback: 5% of 39 = 0.05(39) = 1.95. 39 + 1.95 = 40.95.
Incorrect Feedback: 5% of 39 = 0.05(39) = 1.95. 39 + 1.95 = 40.95.
Question: If 4 + 9 - 2 = 4 - 2 + 9 + n, what is the value of n?
Answer: 0
Correct Feedback: Simplifying each side, we have 11 = 11 + n. If we
subtract 11, we have n = 0.
Incorrect Feedback: Simplifying each side, we have 11 = 11 + n. If we
subtract 11, we have n = 0.
Question: 4/5 = ____
Which ratio will form a proportion with 4/5?
Answer: 6/7.5
Correct Feedback: Cross multiplying 4/5 = 6/7.5, we have 30 = 30. This
proves that the two are proportional.
Incorrect Feedback: Cross multiplying 4/5 = 6/7.5, we have 30 = 30. This
proves that the two are proportional.