6M Honors Unit 7 2024

Charlie walks no more than 30 dogs on Mondays. Ms. Gonzales has 5 dogs that Charlie walks. The inequality shown can be used to find x, the number of dogs Charlie can walk on Monday in addition to Ms. Gonzales’ dogs.

x + 5 ≤ 30

Pick an inequality to represent all possible values of x.

• x≤25

• 5≤ 30+x

• x≤30

• x≥25

Answer explanation

Subtract 5 from both sides of the inequality to isolate x. Do not change the direction of the inequality sign.

Joy has $500 in her checking account. She wants to spend part of this money on a iPhone. She wants to have at least $150 left in her checking account after buying the iPhone . The inequality shown can be used to find t , the amount of money in dollars that Joy can spend on the iPhone.

 

t + 150 ≤ 500

 

Which inequality represents all possible values of t ?

Answer explanation

Subtract 150 from both sides.

• b ≤ 39

• b ≥ 12

• b ≤ 12

• b ≥ 108

Answer explanation

The area is less than or equal to 36. Base times height equals area.

Divide by the height.

Mr. Brook’s truck can travel no more than 505 miles on one full tank of gasoline. After filling up the tank with gasoline, he traveled 189 miles in the truck.

Which inequality represents all possible values of m, the number of miles Mr. Brooks can travel in the truck with the remaining gasoline in the tank?

Answer explanation

Write the inequality first.

m ≤ 505 - 189

Which inequality is true if

p = 3.4

?

Answer explanation

Replace p with 3.4 and solve

Carl reads 2 books each month. Which number line best represents the number of months it will take him to read at least 28 books? 

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Lucy has a goal of walking at least 20 miles. She walks at a rate of 4 miles per hour. Which inequality can Lucy use to find h, the number of hours she should walk in order to meet or exceed her goal?

• 4h ≥ 20

• 4h ≤ 20

• h + 4 ≥ 20

• h + 4 ≤ 20

• James placed x cards in 15 piles, and there were no more than 5 cards in each pile.

• James divided x pieces of paper among 15 students, and each student received fewer than 5 pieces of paper.

• James separated x shirts into 5 stacks, and each stack had at least 15 shirts.

• James shared 15 markers with x classmates, and each classmate had fewer than 5 markers.

• Joe divided x pencils into 13 boxes, and there were at most 8 pencils in each box.

• Joe poured x ounces of soda into 13 glasses, and each glass had no less than 8 ounces of soda.

• Joe separated x books on 13 shelves, and there were more than 8 books on each shelf.

• Joe shared x cupcakes between 13 people, and each person got less than 8 cupcakes.

• w<-13

• w>-13

• w>13

• w<13