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Simplifying Expressions and Solving Equation Word Problems Practice Questions

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Updated on Oct 3, 2011

To review these concepts, go to Simplifying Expressions and Solving Equation Word Problems Study Guide.

Simplifying Expressions and Solving Equation Word Problems Practice Questions

Practice 1

Problems

Simplify each of the following expressions:

  1. 4x + 10x = _____
  2. 20y – 3y = _____
  3. –9x2 + 6x2 – 2x = _____
  4. 2(x – 4) = _____
  5. 7(2y + 5) = _____

Solutions

  1. 14x
  2. 17y
  3. –3x2 – 2x
  4. 2x – 8
  5. 14y + 35

Practice 2

Problems

Solve each of the following equations.

  1. x + 10 = 25
  2. 3x – 5 = 10
  3. 12x – 3x = 18
  4. 5(x + 1) = 30
  5. 2x + 10 = 3(x – 4)

Solutions

  1. x + 10 – 10 = 25 – 10
  2. x = 15

  3. 3x – 5 + 5 = 10 + 5
  4. 3x = 15

    x = 5

  5. 12x – 3x = 18
  6. 9x = 18

    x = 2

  7. 5(x + 1) = 30
  8. 5x + 5 = 30

    5x + 5 – 5 = 30 – 5

    5x = 25

    x = 5

  9. 2x + 10 = 3(x – 4)
  10. 2x + 10 = 3x – 12

    2x – 2x + 10 = 3x – 2x – 12

    10 = x – 12

    10 + 12 = x – 12 + 12

    x = 22

Practice 3

Problems

  1. Six times a number is equal to 300. What is the number?
  2. A number decreased by 7 is equal to the product of 4 and 10. What is the number?
  3. The sum of five and a number is equal to twice the number. What is the number?
  4. Three times the sum of a number and 1 is equal to 21. What is the number?
  5. Thirty-one minus a number is the same as twice a number plus 10. What is the number?

Solutions

  1. Read and understand the question. This question is looking for a number when clues about this number are given.
  2. Make a plan. Translate the statement into equation form. Then, solve the equation using the equation solving steps.

    Carry out the plan. Let x = a number. The key phrase six times a number is written as 6x, so the equation is 6x = 300. Divide each side by 6 to get the variable alone.

      x = 50

    Check your answer. Check your solution by substituting the answer into the equation.

      6x = 300

    becomes

      6(50) = 300
      300 = 300

    This answer is checking.

  3. Read and understand the question. This question is looking for a number when clues about this number are given.
  4. Make a plan. Translate the statement into equation form. Then, solve the equation using the equation solving steps.

    Carry out the plan. Let x = a number. The key phrase decreased by means subtraction, so the first part of the statement translates to x – 7. In the second part of the sentence, the key word product means multiplication, so multiply 4 by 10 to get 40. The entire equation is x – 7 = 40. Get the variable alone by adding 7 to each side. The equation simplifies to x = 47.

    Check your answer. Check your solution by substituting the answer into the equation.

      x – 7 = 4 × 10

    becomes

      47 – 7 = 40
      40 = 40

    This answer is checking.

  5. Read and understand the question. This question is looking for a number when clues about this number are given.
  6. Make a plan. Translate the statement into equation form. Then, solve the equation using the equation solving steps.

    Carry out the plan. Let x = a number. The key word sum means addition, so the first part of the statement translates to x + 5. In the second part of the sentence, twice the number is written as 2x. The entire equation is x + 5 = 2x. Get the variables on one side of the equation by subtracting x from each side.

      xx + 5 = 2xx

    The equation simplifies to

      5 = x

    Check your answer. Check your solution by substituting the answer into the equation.

      x + 5 = 2x

    becomes

      5 + 5 = 2(5)
      10 = 10

    This answer is checking.

  7. Read and understand the question. This question is looking for a number when clues about this number are given.
  8. Make a plan. Translate the statement into equation form. Then, solve the equation using the equation solving steps.

    Carry out the plan. Let x = a number. The key word sum means addition, so the sum of a number and 1 is written as x + 1. Multiply this expression by 3 and set it equal to 21. The statement translates to

      3(x + 1) = 21

    Apply the distributive property.

      3x + 3 = 21

    Subtract 3 from each side of the equation to get 3x = 18. Next, divide each side by 3 to get the variable alone.

      x = 6

    Check your answer. Check your solution by substituting the answer into the equation.

      3(x + 1) = 21

    becomes

      3(6 + 1) = 21
      3(7) = 21
      21 = 21

    This answer is checking.

  9. Read and understand the question. This question is looking for a number when clues about this number are given.
  10. Make a plan. Translate the statement into equation form. Then, solve the equation using the equation solving steps.

    Carry out the plan. Let x = a number. The first part of the statement translates to 31 – x. In the second part of the sentence, twice a number plus 10 is written as 2x + 10. The entire equation is

      31 – x = 2x + 10

    Get the variables on one side of the equation by adding x to each side.

      31 – x + x = 2x + x + 10

    The equation simplifies to 31 = 3x + 10

    Subtract 10 from each side of the equation to get 21 = 3x. Next, divide each side by 3 to get the variable alone.

      x = 7

    Check your answer. Check your solution by substituting the answer into the equation.

      31 – x = 2x + 10

    becomes

      31 – 7 = 2(7) + 10
      24 = 14 + 10
      14 = 14

    This answer is checking.

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