1. Solve x + 15 ≥ 3. Make sure to write your inequality so that x comes first.
2. Solve x+212<8 . Make sure to write your inequality so that x comes first.
3. Willow solved an inequality and graphed the solution on the number line. Which of the following inequalities did she solve?
(A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. An open circle is marked on the number line at 4.5. A line is drawn from the circle toward negative 10 with an arrow at the end.)
A. x + 2 1\2 < 2 1\2
B. x − 1.5 ≤ 3
C. x − 2 1\3 < 2 1\6
D. x + 1.25 ≤ 5.75
4. Solve 5x<12 . Write the improper fraction in your answer as a mixed number. Make sure to write your inequality so that x comes first.
5. Solve 3.4x≥23.8 . Make sure to write your inequality so that x comes first.
6. Paolo solved an inequality and graphed the solution on the number line. Which of the following inequalities did he solve?
(A number line ranges from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line at 4. A leftward arrow is marked on the number line that originates at the open circle and goes beyond negative 10.)
A 2.1x < 8.4
B 3.7x > 14.8
C 2.8x < 10.5
D 4.9x > 19.6
7. Solve 8x−14≤10 . Make sure to write your inequality so that x comes first
8. Solve 5.14x+2.25>15.1 . Write the rational number in your answer in decimal form to the tenths place. Make sure to write your inequality so that x comes first.
9. Preston solved an inequality and graphed the solution on the number line. Which of the following inequalities did he solve?
(A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line between 1 and 2. A rightward arrow is marked on the number line that originates at the closed point and goes beyond 10.)
A 2.1x + 5.6 ≥ 8.75
B 0.9x + 2.8 ≤ 5.95
C 5.6x − 18.9 ≤ 0.7
D 3.4x − 1.2 ≥ 4.75
10. Fifteen less than four times a number is more than 49. What are all the possible values of the number? Write an inequality that could be used to solve this problem. Use the letter x as your variable and write your x term first.
11. Youssef is taking a trip on an airplane. He knows that to avoid extra fees his suitcase must weigh under 50 pounds. The suitcase with his clothes weighs 35 pounds. He has room, so he decides to pack some books for his trip, too. Each book weighs on average 1.2 pounds. How many books could he bring on the trip? He writes the inequality 1.2b + 35 < 50 , where b equals the number of books, to help figure this out. Solve his inequality. Use the letter b as your variable and write your b term first.
12. Marjam has a goal of taking at least 10,000 steps today. According to her pedometer, she got 2,500 steps in the morning. There are 10 hours left in the day. How many steps will she need to get each hour (assume she walks the same number of steps each hour) for the rest of the day to meet her goal? Solve this problem. Which graph most clearly communicates the solution?(1 point)
Responses
A. An illustration shows a number line labeled Marjam’s Steps per Hour for the Remainder of the Day. The number line ranges from 0 to 900 in 100 unit increments. A closed point is plotted at 750. A line extends from that point to the right and goes past 900.
Image with alt text: An illustration shows a number line labeled Marjam’s Steps per Hour for the Remainder of the Day. The number line ranges from 0 to 900 in 100 unit increments. A closed point is plotted at 750. A line extends from that point to the right and goes past 900.
B. A number line ranges from 0 to 900 in 100 unit increments. An open point is labeled and plotted at 750. A line extends from that point to the right and goes past 900.
Image with alt text: A number line ranges from 0 to 900 in 100 unit increments. An open point is labeled and plotted at 750. A line extends from that point to the right and goes past 900.
C. A number line ranges from 0 to 900 in 100 unit increments. An open point is labeled and plotted at 750. A line extends from that point to the right and goes past 900.
Image with alt text: A number line ranges from 0 to 900 in 100 unit increments. An open point is labeled and plotted at 750. A line extends from that point to the right and goes past 900.
D. A number line is marked with 10 equidistant tick marks. An open point is plotted halfway between the eighth and ninth tick marks from the left. A line extends from that point to the right and goes past the last tick mark.
Image with alt text: A number line is marked with 10 equidistant tick marks. An open point is plotted halfway between the eighth and ninth tick marks from the left. A line extends from that point to the right and goes past the last tick mark.
13. What inequality is shown on the graph? Write your inequality with the variable coming first.
A number line ranges from 16 to 32 in 1 unit increments. An open point is labeled and plotted at 25.60. A line extends from that point to the right and goes past 32. The number line is labeled Bogdan's Earnings Per Yard.
Use the letter m for the variable. Write your answer using a decimal number.
14. Lily is saving up to buy a cellphone. She needs to save at least $300 before she is able to buy the phone. Her grandfather gives her $40, and she earns $65 tutoring after school each week. Write an inequality for the number of weeks Lily will need to save to have at least $300, and describe the solutions.
__ x + __≥ __ , where x is the number of weeks Lily will need to save. Lily must save for at least __ weeks to have at least $300.
TYYYY:D!!!
1. x ≥ -12
2. x < -204
3. A. x + 2 1/2 < 2 1/2
4. x < 12/5 (or x < 2 2/5)
5. x ≥ 7
6. A. 2.1x < 8.4
7. x ≤ 3
8. x > 2.5
9. B. 0.9x + 2.8 ≤ 5.95
10. 4x - 15 > 49 (or x > 16)
11. b < 12
12. The graph most clearly communicating the solution is A. An illustration shows a number line labeled Marjam’s Steps per Hour for the Remainder of the Day with a closed point plotted at 750 and a line extending from that point to the right past 900.
13. m ≥ 25.60
14. 65x + 40 ≥ 300, where x is the number of weeks Lily will need to save. Lily must save for at least 5 weeks to have at least $300.