Digits, Grade 8, Volume 1, Homework Helper
  • 11. Error Analysis You and a friend are doing math homework together. You have to solve the equation 5x + 4x − 68 = 34 − 8x. Your friend arrives at the incorrect answer x = −2.

    • a. Find the correct value of x.

    • b. What possible error could your friend have made to get x = −2?

      • A. Your friend should have added 8x to each side of the equation, but instead subtracted 8x from the left side.

      • B. Your friend should have added 5x and 4x to get a sum of 9x, but instead got a sum of 10x.

      • C. Your friend should have added 68 to each side of the equation, but instead subtracted 68 from the right side.

  • 12. Multiple Representations You can use algebra tiles to model and solve the equation 8x + 4 = 4x + 12.

    Left side: eight x tiles and four 1 tiles. Right side: four x tiles and twelve 1 tiles.

    • a. What are two other ways to write the equation?

      • A. 8x + 8 = −4x and 4x − 4 = 12

      • B. −8x = 8 − 4x and 8x + 8 = −4x

      • C. 8x + 8 = 4x and 4x + 12 = 4

      • D. 8x − 8 = 4x and 4x + 4 = 12

    • b. Solve the equation to find the value of x.

  • 13. Challenge The price of stock A at 9 A.M. was $12.73. Since then, the price has been increasing at the rate of $0.06 each hour. At noon the price of Stock B was $13.48. It begins to decrease at the rate of $0.14 each hour. If the two rates continue, in how many hours will the prices of the two stocks be the same? Round to the nearest tenth as needed.

  • 14. Consider the equation x over 30 , equals . fraction open 195 minus x close , over 20 end fraction .

    • a. Which of these descriptions matches the given equation?

      • A. Divide a number by 30. The result is the same as dividing the difference between 195 and the number by 20.

      • B. Multiply a number by 30. The result is the same as multiplying the number by 20 and subtracting the quotient from 195.

      • C. Multiply a number by 30. The result is the same as multiplying the difference between 195 and the number by 20.

      • D. Divide a number by 30. The result is the same as dividing the sum of 195 and the number by 20.

      • E. Divide a number by 30. The result is the same as dividing the number by 20 and subtracting the quotient from 195.

      • F. Multiply a number by 30. The result is the same as multiplying the sum of 195 and the number by 20.

    • b. Describe a real-world situation that could be represented by the equation.


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Table of Contents

Digits, Grade 8, Volume 1, Homework Helper Unit A: Number and Operations Unit B: Proportionality Unit C: Expressions, Equations, and Relationships English/Spanish Glossary Formulas Math Symbols Formulas Measures Properties