1st term math RExam
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Questions and Answers

Which equation represents this sentence? Four times the sum of a number x and a number y is equal to 20.

  • 4x + y = 20
  • 4xy = 20
  • 4 + x + y = 20
  • 4(x + y) = 20 (correct)

    • Solve x – 5 = 21. What is x?

    26

    Solve 21 = 3p – 6. What is p?

  • 9 (correct)
  • 24
  • 13
  • 5

    • Solve 5 = 10 for x. Assume that a ≠ 0. Find x in 15 + ax.

    <p>x = −13/a</p> Signup and view all the answers

    Solve 4x – 5 = 41. What is x?

    <p>11.5</p> Signup and view all the answers

    Solve 4(x + 9) = 6x – 4. What is x?

    <p>16</p> Signup and view all the answers

    Solve 3 |y + 6| = 30. What are the possible values of y?

    <p>{–12, 8}</p> Signup and view all the answers

    Solve x + 15 = 2. 10 5. What is x?

    <p>–13</p> Signup and view all the answers

    Solve x = 21/144. What is x?

    <p>0.1458</p> Signup and view all the answers

    Solve 2x + 12/5 = 4y for x. What is x?

    <p>x = 10y − 12</p> Signup and view all the answers

    Which equation represents this sentence? The sum of 5 times a number m and 12 is equal to 27.

    <p>5m + 12 = 27</p> Signup and view all the answers

    Solve n − 8 = 5 and identify the property of equality used. What are the results?

    <p>–13; Subtraction Property of Equality</p> Signup and view all the answers

    Solve z + 12 = –3. What is z?

    <p>–15</p> Signup and view all the answers

    Solve 1t = 10. 5. What is t?

    <p>5</p> Signup and view all the answers

    If 3x – 6 = 42, what is the value of x?

    <p>12</p> Signup and view all the answers

    Solve 8 = 11 – 3y. What is y?

    <p>1</p> Signup and view all the answers

    Solve 5 – kx = 9 for x. Assume that k ≠ 0. What is x?

    <p>x = −4/k</p> Signup and view all the answers

    Solve 3x + 1 = 4x – 8. What is x?

    <p>9</p> Signup and view all the answers

    Solve 5(2y + 1) = 4y + 10. What is y?

    <p>3/2</p> Signup and view all the answers

    Solve 12/b = 10/15. What is b?

    <p>18</p> Signup and view all the answers

    Solve 3/(x+4) = (x − 2)/4. What is x?

    <p>4</p> Signup and view all the answers

    Which equation represents this sentence? The sum of five times a number and seven is equal to twelve.

    <p>5n + 7 = 12</p> Signup and view all the answers

    Solve 1/a = 12/2. What is a?

    <p>6</p> Signup and view all the answers

    Solve p + 8 = 15. What is p?

    <p>7</p> Signup and view all the answers

    Solve bx − 4 = 5 for x. Assume that b ≠ 0. What is x?

    <p>x = 1/b</p> Signup and view all the answers

    Solve 3y + 6 = 18. What is y?

    <p>4</p> Signup and view all the answers

    Solve 4m + 5 = 2m + 45. What is m?

    <p>20</p> Signup and view all the answers

    Solve 5(r + 3) = 3r + 35. What is r?

    <p>4</p> Signup and view all the answers

    Study Notes

    Solving Equations

    • Solving for a variable: To solve an equation, isolate the variable on one side of the equation by performing the same operation on both sides.
    • Using properties of equality:
      • Addition Property of Equality: Adding the same number to both sides of an equation does not change the solution.
      • Subtraction Property of Equality: Subtracting the same number from both sides of an equation does not change the solution.
      • Multiplication Property of Equality: Multiplying both sides of an equation by the same nonzero number does not change the solution.
      • Division Property of Equality: Dividing both sides of an equation by the same nonzero number does not change the solution.
    • Solving multi-step equations: Combine like terms, use the properties of equality, and simplify to isolate the variable.
    • Solving equations with absolute values:
      • Remember absolute value represents distance from zero.
      • Solve two separate equations, one with the expression inside the absolute value being positive and the other being negative.

    Writing Equations from Sentences

    • Identify the unknown: Determine the variable that represents the unknown quantity.
    • Translate words into symbols: Use mathematical symbols (+, -, ×, ÷, =) to represent the relationships described in the sentence.
    • Combine expressions: Combine the expressions according to the relationship expressed in the sentence.
    • Write the equation: Use the given information to write the equation in a standard mathematical format.

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