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. • 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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