1. What are the solutions of 7x + 16 > 4x − 2? (Simplify your answer.)
2. Two water tanks are being filled. The water in tank A is 4 inches deep, and the depth of the water increases 4 inches every hour. The water in tank B is 7 inches deep, and the depth is increasing by 2 inches every hour. After how many hours will the water in tank A be deeper than the water in tank B?
a. Describe the inequality 8x < 7x + 9 in words.
A. Nine more than a number times seven is less than eight times the number.
B. A number times eight is less than seven times the number plus nine.
C. Seven times a number is less than eight times the number plus nine.
D. Multiply a number by eight. The result is at least nine times the number plus seven.
b. Describe a real-world situation that could be represented by the inequality.
4. Savings Accounts At the beginning of the year, Ethan has $700 in his savings account and Faith has $1,140 in her savings account. Each month, Ethan deposits an additional $25 in his account, while Faith withdraws $15 from her account. Ignoring any interest earned, after how many months will Ethan's account have a greater balance than Faith's account?
5. When 5 is added to the difference between six times a number and 8, the result is greater than 13 added to 5 times the number. Find all such numbers.
6. Error Analysis On a recent math test, the students were asked to write and solve an inequality for the given statement, using x to represent the missing number. Alex wrote the inequality 9 − 5x < 7x and said the solutions are x greater than , 3 fourths .
9 subtracted from 5 times a number is less than 7 times the number.
a. Which inequality represents the statement?
A. 9x − 5 > 7x
B. 5 − 9x < 7x
C. 5x − 9 < 7x
D. 5x − 9 > 7x
b. Solve the inequality from part (a). Select the correct choice below and replace the box with a number to complete your choice.
A. x >
B. x ≤
C. x <
D. x ≥
c. What error might Alex have made?
A. Alex added 9 to both sides of the inequality. He should have subtracted.
B. Alex wrote the wrong inequality for the statement.
C. Alex forgot to reverse the sign in the inequality.
D. Alex subtracted 7x from both sides of the inequality. He should have added.
7. Think About the Process At a park, it costs $9.25 an hour to rent a bicycle. It costs $5.75 an hour to rent a scooter. Aaron has a coupon for $7 off the rental of a bicycle. He wants to know after how many hours it will cost more to rent the bicycle than the scooter.
a. Write an inequality that models this situation.
A. 9.25x − 7 < 5.75x
B. 5.75x − 7 > 9.25x
C. 9.25x − 7 > 5.75x
D. 9.25x − 5.75x < 7
b. After how many hours will it cost more to rent the bicycle than the scooter?