Digits, Grade 8, Volume 1, Homework Helper

### 6-3: TEKS Practice

• 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?

• 3.

• 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.

• 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?

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