Equations & Inequalities

Which equation best represents the relationship between x and y in the graph?

• y = 3x − 2

• y = −2x + 3

Jeff bought a bottle of water for $2. He also bought some hot dogs for $3 each. Jeff did not spend more than $14 on the hot dogs and the bottle of water. Which inequality can be used to find h, the number of hot dogs that Jeff could have bought?

• 3h - 2 ≤ 14

• 3h + 2 ≤ 14

• 3h - 2 ≥ 14

• 3h + 2 ≥ 14

Which situation is best represented by the following equation?

45w + 123.95 = 753.95

• Erica paid $753.95 for dance classes. She paid a $123.95 registration fee and $45 for each week she was enrolled in the classes. What is w, the number of weeks Erica was enrolled in dance classes?

• Erica paid $753.95 for dance classes. She paid a $45 registration fee and $123.95 for each week she was enrolled in the classes. What is w, the number of weeks Erica was enrolled in dance classes?

• Erica and her sister paid $753.95 for dance classes. Erica paid $123.95 for each week she was enrolled in the classes, and her sister paid $45 for each week she was enrolled in the classes. What is w, the number of weeks Erica and her sister were enrolled in dance classes?

• Erica paid $753.95 for dance classes. She paid $123.95 for each week she was enrolled in the classes after using a coupon that gave her $45 off the price per week. What is w, the number of weeks Erica was enrolled in dance classes?

Which situation can be represented by this inequality?

1.25x - 6.50 > 50

• Stefan spends $6.50 on supplies for a lemonade stand and sells each cup of lemonade for $1.25. What is x, the number of cups of lemonade Stefan must sell to earn a profit of more than $50?

• Stefan has a balance of $6.50 in his savings account and deposits $1.25 each week. What is x, the number of weeks Stefan must deposit $1.25 in order to have a balance of more than $50 in his savings account?

• Stefan earns 1.25% interest on the balance in his checking account and has to pay a monthly charge of $6.50. What is x, the balance that Stefan must have in his checking account in order to have an ending balance greater than $50 after interest and fees?

• Stefan charges $1.25 for gasoline plus $6.50 per hour for mowing lawns. What is x, the number of hours he has to mow lawns to earn more than $50?

A fish is swimming at a constant rate toward the ocean floor. The equation y = -7x -3 can be used to represent this situation, where y is the depth of the fish in meters below sea level and x is the number of seconds the fish has been swimming. Which statement best describes the depth of the fish, given this equation?

• From a starting position of 7 meters below sea level, the fish is descending 3 meters per second.

• From a starting position of 7 meters below sea level, the fish is ascending 3 meters per second.

• From a starting position of 3 meters below sea level, the fish is descending 7 meters per second.

• From a starting position of 3 meters below sea level, the fish is ascending 7 meters per second

George started a coin collection. His dad gave him 75 coins. Each month he will add 20 coins to the collection. Which equation can be used to find y, the total number of coins in George’s collection after x months?

• y = 75x + 20

• y = 20x + 75

• y = 75x − 20

• y = 20x − 75

A pilot takes a taxi from the airport to a hotel. The taxi driver charges a $2.50 initial charge plus $2.65 per mile. Which equation can be used to find y, the total cost of the trip, if x represents the number of miles of the trip?

• y = 2.50x + 2.65

• y = 2.65(x + 2.50)

• y = 2.65x - 2.50

• y = 2.65x + 2.50

Which number line represents the solution to the inequality 125x + 200 ≥ 1,200?

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The model represents an inequality. What is the solution set for the inequality?

• x ≤ -5

• x ≤ 5

• x ≤ 1

• x ≤ -14

What is the solution set for -4x - 10 ≤ 2?

• x ≤ -3

• x ≥ -3

• x ≤ 2

• x ≥ 2