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.
Note: You will find the option to add a >
>
, <
<
, ≥
≥
, or ≤
≤
symbol in the Comparison (<)
(
<
)
keyboard.
1.2b + 35 < 50
To solve for b, we need to subtract 35 from both sides of the inequality:
1.2b < 50 - 35
1.2b < 15
To isolate b, divide both sides of the inequality by 1.2:
b < 15 / 1.2
b < 12.5
Therefore, Youssef can bring a maximum of 12 books on his trip.
Solve this problem by writing and solving an inequality. Five more than four times a number is less than 25. What are the possible values of the number? Show your work.
Let's start by writing the inequality for the problem.
Five more than four times a number (let's call it x) is less than 25. Mathematically, we can write this as:
4x + 5 < 25
Now, let's solve the inequality.
Subtract 5 from both sides of the inequality:
4x < 25 - 5
4x < 20
To isolate x, divide both sides of the inequality by 4:
x < 20/4
x < 5
Therefore, the possible values for the number x in this problem are any number less than 5.
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.(2 points)
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
The inequality for the number of weeks Lily will need to save to have at least $300 can be written as:
65x + 40 ≥ 300
In this inequality, x represents the number of weeks Lily will need to save. To solve the inequality, we can perform the following steps:
1. Subtract 40 from both sides of the inequality:
65x ≥ 260
2. Divide both sides of the inequality by 65:
x ≥ 4
The solution to the inequality is x ≥ 4.
This means that Lily will need to save for at least 4 weeks in order to have at least $300. Any number of weeks equal to or greater than 4 will satisfy the condition.