Can you check these inequalities?
1. Chancellor is saving $15 each week for at least n weeks to buy a skateboard that cost $150. Write an inequality to represent this real life situation.
Ans: 15n >= 150
2. Write an inequality to represent the possible speed allowed fi the current highway speed limit is 70 miles per hour.
Ans: s <= 70
3. Bonnie has to raise $150 or more to go to Summer Swim camp. She has raised $30 so far. Write an inequality to represent the amount of money, m, that Bonnie still needs to raise.
Ans: m + 30 >= 150
4. Solve: 8 > x + 3
Ans: 8 > x + 3
= -3 > x -3
= 5 > x or x < 5
5. Sarah's bank account has less than 7 dollars in it. Wrate a set of at least four values that represents the amount of money she has in her account to make the inequality S < 7 true.
Ans: S = 3, 4, 5, 6
6. Desean's teacher told him that he needed to read more than 30minutes each day. Write an inequality that represents the time he needs to read daily if m represents the number of minutes.
Ans: m > 30
7. Solve 1/3x <= 1
1/3x <= 1
3/1)(1/3x) <= 1 (3/1)
Ans: x <= 3
8. SOlve: 2 <= x-6
+6 +6
Ans: 8 <= x or x>= 8
9. Is the inequality 15 <= x equivalent to x >= 15. Explain.
Ans: They are the same. 15 <= x can be rewritten as x >= 15.
10. Tino's Pizza charges $9 for a cheese pizza. Eileen has $45 to buy pizza for the Spanish class. Write and solve an inequality to find the maximum number of pizzas she can buy.
Ans: 9p <= 45
p = 5 pizzas
1,2, and 3 are ok
#4 has the right answer, but I don't like the way you stated your solution
First of all, don't put equal signs in front of each new line when solving.
Youre 2nd last line has no relation to the problem, what happened to the 5 ?
here is how I would write it:
8 > x+3
8-3 > x+3-3
5 > x or x < 5
#5,6 , ok
#7 , your solution looks more complicated than it has to be
(1/3)x ≤ 1
times 3
x ≤ 3 or x ≥ 3
#8 , I sure don't like the line that says:
+6 + 6, I have no idea what that is
my way:
2 ≤ x-6
2+6 ≤ x-6+6
8 ≤ x or x ≥ 8
#9, 10 ok
Ok.. for #4, i was trying to show that i subtracted 3 from both sides; #7, I was trying to show that I multiplied both sides by 3; and #8 was trying to show that I added 6 to both sides. I agree that I like how you showed it in #8. Thanks Reiny!
solve
missed out this workshop, I'll be shanirg in the next few posts some of the fatal mistakes (Quadratic Equations, Logarithms) you must NEVER make! Let's get the house rules right on day 1 before we begin
1. The inequality to represent this situation is 15n >= 150. To get this answer, you can set up the equation, where "n" represents the number of weeks and "15" represents the amount saved each week. Multiply 15 by "n" to get the total amount saved after "n" weeks, then set that amount greater than or equal to the cost of the skateboard, which is $150.
2. The inequality to represent the speed allowed is s <= 70. To get this answer, you can set up the equation, where "s" represents the speed allowed. Since the speed allowed should not exceed 70 miles per hour, you set "s" less than or equal to 70.
3. The inequality to represent the amount of money Bonnie still needs to raise is m + 30 >= 150. To get this answer, you can set up the equation, where "m" represents the amount of money Bonnie still needs to raise. Add $30 to the amount Bonnie has raised so far, then set that total amount greater than or equal to the cost of going to Summer Swim camp, which is $150.
4. To solve the inequality 8 > x + 3, you need to isolate the variable "x" on one side of the inequality sign. Subtract 3 from both sides, and you have -3 > x. Reversing the inequality sign gives x < -3.
5. To find a set of values that represents the amount of money Sarah has in her account, where S < 7, you can choose various amounts less than 7 dollars. For example, S = 3, 4, 5, or 6 would all be valid values that make the inequality S < 7 true.
6. The inequality to represent the time Desean needs to read daily is m > 30. To get this answer, you can set up the equation, where "m" represents the number of minutes. Since Desean needs to read more than 30 minutes each day, you set "m" greater than 30.
7. To solve the inequality 1/3x <= 1, you need to isolate the variable "x" on one side of the inequality sign. Multiply both sides by 3/1 (or 3), and you have x <= 3.
8. To solve the inequality 2 <= x - 6, you need to isolate the variable "x" on one side of the inequality sign. Add 6 to both sides, and you have 8 <= x (or x >= 8).
9. The inequality 15 <= x is equivalent to x >= 15. This is because "15 <= x" means x is greater than or equal to 15, while "x >= 15" means x is also greater than or equal to 15. The two inequalities represent the same relationships between the numbers.
10. To find the maximum number of pizzas Eileen can buy, you can set up the inequality 9p <= 45, where "p" represents the number of pizzas. Divide both sides of the inequality by 9, and you have p <= 5. Therefore, Eileen can buy a maximum of 5 pizzas with $45.