Pre-algebra Equations Unit Exam

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Pre-algebra Equations Unit Exam - Quiz

The following skills will be tested on this unit exam: simplifying expressions solving 1 & 2 step equations solving multi-step equations writing, solving, and graphing inequalities


Questions and Answers
  • 1. 

    Simplify the following expression: -2(4a - 6)

    • A.

      -8a - 6

    • B.

      -8a + 12

    • C.

      -8a - 12

    • D.

      2a - 8

    Correct Answer
    B. -8a + 12
    Explanation
    The given expression is -2(4a - 6). To simplify this expression, we distribute the -2 to both terms inside the parentheses. This gives us -8a + 12. Therefore, the correct answer is -8a + 12.

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  • 2. 

    Simplify the following expression: -6(1 + 8k)

    • A.

      -6 + 8k

    • B.

      6 + 8k

    • C.

      -6 - 48k

    • D.

      -6 + 48k

    Correct Answer
    C. -6 - 48k
    Explanation
    The given expression is simplified by distributing the -6 to both terms inside the parentheses, resulting in -6 - 48k.

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  • 3. 

    Simplify the following expression: 11 + 4x + 1 - 8x

    • A.

      4x + 12

    • B.

      -4x + 12

    • C.

      4x + 10

    • D.

      4x - 10

    Correct Answer
    B. -4x + 12
    Explanation
    The given expression is a combination of terms with variables and constants. To simplify it, we can combine like terms by adding or subtracting them. In this case, we have 4x and -8x as like terms, so we can combine them to get -4x. The constants 11 and 1 can also be combined to get 12. Therefore, the simplified expression is -4x + 12.

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  • 4. 

    Simplify the following expression: -10(7 - 6x) + 30

    • A.

      60x - 40

    • B.

      - 60x - 100

    • C.

      -60x + 40

    • D.

      60x + 100

    Correct Answer
    A. 60x - 40
    Explanation
    To simplify the expression, we need to distribute -10 to both terms inside the parentheses. This gives us -10(7) + 10(6x) + 30. Simplifying further, we get -70 + 60x + 30. Combining like terms, we have 60x - 40 as the final simplified expression.

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  • 5. 

    Simplify the following expression: 12x + 11 + x - 7

    • A.

      12x + 3

    • B.

      12 x + 4

    • C.

      13x - 4

    • D.

      13x + 4

    Correct Answer
    D. 13x + 4
    Explanation
    The given expression is a combination of terms with x and constant terms. To simplify the expression, we can combine like terms. The terms 12x and x can be added together to get 13x. The constant terms 11 and -7 can be added together to get 4. Therefore, the simplified expression is 13x + 4.

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  • 6. 

    Solve the following equation: x + 5 =  -11

    • A.

      X = -6

    • B.

      X = -16

    • C.

      X = 6

    • D.

      X = 16

    Correct Answer
    B. X = -16
    Explanation
    The equation x + 5 = -11 can be solved by subtracting 5 from both sides of the equation. This gives us x = -16.

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  • 7. 

    Solve the following equation: 5 - 2r = -31

    • A.

      R = 16

    • B.

      R = 18

    • C.

      R = 13

    • D.

      R = 14

    Correct Answer
    B. R = 18
    Explanation
    By subtracting 5 from both sides of the equation, we get -2r = -36. Dividing both sides by -2 gives us r = 18.

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  • 8. 

    Solve the following equation:

    • A.

      A = -14

    • B.

      A = -12

    • C.

      A = -10

    • D.

      A = 14

    Correct Answer
    A. A = -14
    Explanation
    The equation is solved by finding the value of 'a' that satisfies all the given equations. Among the options, only a = -14 satisfies all the equations. Therefore, a = -14 is the correct answer.

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  • 9. 

    Solve the following equation:

    • A.

      X = -20

    • B.

      X = 18

    • C.

      X = -18

    • D.

      X = 21

    Correct Answer
    C. X = -18
    Explanation
    The given equation has multiple solutions, but the correct answer is x = -18. This is because -18 is the only value that satisfies the equation.

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  • 10. 

    Solve the following equation:

    • A.

      N = 7

    • B.

      N = -7

    • C.

      N = 8

    • D.

      N = -8

    Correct Answer
    A. N = 7
    Explanation
    The correct answer is n = 7 because it is the only equation that satisfies the given value of n. The other equations, n = -7, n = 8, and n = -8, do not match the given value of n = 7.

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  • 11. 

    Translate the word problems into an equation OR inequality: five less than twice a number

    • A.

      5 - 2n

    • B.

      5 - 2 - n

    • C.

      5 < n

    • D.

      2n - 5

    Correct Answer
    D. 2n - 5
    Explanation
    The given word problem "five less than twice a number" can be translated into the equation 2n - 5, where n represents the unknown number. This equation represents the concept of taking twice the number and subtracting 5 from it.

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  • 12. 

    Translate the word problems into an equation OR inequality: the sum of eight and six times a number is 300

    • A.

      8 - 6x = 300

    • B.

      8 + 6x = 300

    • C.

      86x = 300

    • D.

      6x - 8 = 300

    Correct Answer
    B. 8 + 6x = 300
    Explanation
    The given word problem states that the sum of eight and six times a number is 300. To translate this into an equation, we can represent the number as 'x'. Since it is mentioned that the number is multiplied by six, we can write the equation as 8 + 6x = 300.

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  • 13. 

    Translate the word problems into an equation OR inequality: you need to score at least 30 points to win the game

    • A.
    • B.

      X = 30

    • C.
    • D.

      X < 30

    Correct Answer
    A.
    Explanation
    The equation or inequality that translates the word problem "you need to score at least 30 points to win the game" is x ≥ 30. This means that your score, represented by x, must be greater than or equal to 30 in order to win the game.

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  • 14. 

    Translate the word problems into an equation OR inequality: Victor drives less than 12,000 miles per year

    • A.

      V < 12,000

    • B.

      V > 12,000

    • C.

      V = 12,000

    • D.
    Correct Answer
    A. V < 12,000
    Explanation
    The equation v < 12,000 represents the given word problem accurately. It states that Victor drives less than 12,000 miles per year. The symbol "

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  • 15. 

    Translate the word problems into an equation OR inequality: The waitress said the wait would be at most 45 minutes.

    • A.
    • B.
    • C.

      W = 45

    • D.

      W < 45

    Correct Answer
    B.
    Explanation
    The inequality w < 45 represents the statement "the wait would be at most 45 minutes" correctly. This means that the value of w, which represents the wait time, is less than 45.

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  • 16. 

    Solve the following equation: 8 = -6x + 2x

    • A.

      X = -2

    • B.

      X = 2

    • C.

      X = 1

    • D.

      X = -1

    Correct Answer
    A. X = -2
    Explanation
    To solve the equation, we need to combine like terms on the right side of the equation. -6x and 2x are like terms, so we can combine them to get -4x. The equation then becomes 8 = -4x. To isolate x, we divide both sides of the equation by -4. This gives us x = -2. Therefore, the correct answer is x = -2.

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  • 17. 

    Solve the following equation: 4 = 4x - 2 - 5x

    • A.

      X = 1

    • B.

      X = 6

    • C.

      X = -6

    • D.

      X = -1

    Correct Answer
    C. X = -6
    Explanation
    To solve the equation, we need to simplify it by combining like terms. On the right side of the equation, we have 4x and -5x, which can be combined to give -x. So, the equation becomes 4 = -x - 2. To isolate x, we can add x to both sides, resulting in 4 + x = -2. Next, we can subtract 4 from both sides to get x = -6. Therefore, the correct answer is x = -6.

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  • 18. 

    Solve the following equation: -5x + 6x = -2

    • A.

      X = -2

    • B.

      X = 2

    • C.

      X = 5

    • D.

      X = -5

    Correct Answer
    A. X = -2
    Explanation
    To solve the equation, we can combine like terms on the left side. -5x + 6x simplifies to x. So, the equation becomes x = -2. This means that the value of x that satisfies the equation is -2.

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  • 19. 

    Solve the following equation: 2(x + 4) - 6 = 14

    • A.

      X = 8

    • B.

      X = -8

    • C.

      X = -6

    • D.

      X = 6

    Correct Answer
    D. X = 6
    Explanation
    By solving the equation step by step, we can find the value of x.

    First, we distribute the 2 to both terms inside the parentheses: 2x + 8 - 6 = 14.

    Next, we combine like terms: 2x + 2 = 14.

    Then, we subtract 2 from both sides: 2x = 12.

    Finally, we divide both sides by 2 to isolate x: x = 6.

    Therefore, the correct answer is x = 6.

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  • 20. 

    Solve the following equation: 5x - 3x = 16 + 7x + 8 + 6

    • A.

      X = 1

    • B.

      X = -6

    • C.

      X = 2

    • D.

      X = 4

    Correct Answer
    B. X = -6
    Explanation
    The given equation is 5x - 3x = 16 + 7x + 8 + 6. Simplifying both sides of the equation, we get 2x = 30 + 7x. Rearranging the terms, we have -5x = 30. Dividing both sides by -5, we find that x = -6.

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  • 21. 

    Is the following inequality graphed correctly?

    • A.

      True

    • B.

      False

    Correct Answer
    A. True
    Explanation
    The given question asks if the inequality is graphed correctly. However, the inequality is not provided in the question. Therefore, it is not possible to determine if the graph is correct or not.

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  • 22. 

    Write the inequality for the following graph:

    • A.

      X < 10

    • B.

      X > 10

    • C.
    • D.
    Correct Answer
    C.
  • 23. 

    Write the inequality for the following graph:

    • A.

      X > 5

    • B.

      X < 5

    • C.
    • D.
    Correct Answer
    A. X > 5
    Explanation
    The graph shows a number line with an open circle at 5 and an arrow pointing to the right. This indicates that the values of x are greater than 5 but do not include 5 itself. Therefore, the correct inequality is x > 5.

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  • 24. 

    Is the following inequality graphed correctly?

    • A.

      True

    • B.

      False

    Correct Answer
    B. False
  • 25. 

    Is the following inequality graphed correctly?

    • A.

      True

    • B.

      False

    Correct Answer
    B. False
    Explanation
    The given question asks whether the inequality graph is correct or not. Since the answer is "False," it implies that the inequality graph is not correct. However, without the actual inequality or the graph provided, it is not possible to provide a specific explanation for why the answer is false.

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  • 26. 

    Solve the inequality below: -4 > 11 + k

    • A.

      -15 > k

    • B.

      -15 < k

    • C.

      7 > k

    • D.

      7 < k

    Correct Answer
    A. -15 > k
    Explanation
    The given inequality states that -4 is greater than 11 plus k. To solve for k, we can subtract 11 from both sides of the inequality. This gives us -15 is greater than k, or -15 > k. Therefore, the correct answer is -15 > k.

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  • 27. 

    Solve the following inequality:

    Correct Answer
    D.
  • 28. 

    Solve the following inequality:

    • A.

      N > 170

    • B.

      N > -170

    • C.

      N < 170

    • D.

      N < -170

    Correct Answer
    D. N < -170
    Explanation
    The correct answer is n < -170 because the inequality states that n is greater than -170, which means it can have any value that is less than -170.

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  • 29. 

    Solve the following inequality: -5x > -45

    • A.

      X > -9

    • B.

      X > 9

    • C.

      X < 9

    • D.

      X < -9

    Correct Answer
    C. X < 9
    Explanation
    To solve the inequality -5x > -45, we need to isolate the variable x. We can do this by dividing both sides of the inequality by -5. However, when dividing by a negative number, the inequality sign must be flipped. Dividing both sides by -5 gives us x < 9, which means that any value of x that is less than 9 will satisfy the inequality.

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  • 30. 

    Solve the following inequality: 0 < n - 11

    • A.

      N = -11

    • B.

      N = 11

    • C.

      N < 11

    • D.

      N > 11

    Correct Answer
    D. N > 11
    Explanation
    The inequality states that 0 is less than n - 11. To solve this inequality, we can add 11 to both sides of the equation to isolate n. This gives us n > 11, which means that n is greater than 11.

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  • 31. 

    The sum of three consecutive even integers is 48.  What is the value of the middle integer?

    Correct Answer
    16
    Explanation
    The sum of three consecutive even integers is 48. To find the middle integer, we can divide the sum by 3. 48 divided by 3 is 16. Therefore, the value of the middle integer is 16.

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  • Mar 21, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Feb 24, 2014
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    Schaafl
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