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.