Inequality Word Problems
Dr. B. is saving money to buy a new phone. He has already saved $500 and plans to save an additional $10 each day. He wants to have at least $1200 to buy the phone. How many days does he need to save money to reach his goal? Define your variable.
d = days
x > 4
4x + 3 < 7
x < 1
4 < f + 6 < 5
-2 < f < -1
or
f > -2 and f < -1
x < -1
Dr. B. is saving money to buy a new phone. He has already saved $500 and plans to save an additional $10 each day. He wants to have at least $1200 to buy the phone. How many days does he need to save money to reach his goal? Set up your inequality. Do not solve.
500 + 10d > 1200
x + 4 < -88
x < -92
2x - 5 > - 11
x > -3
p - 2 < -2 OR p - 2 > 1
p < 0 OR p > 3
3x + 4 > -5x - 12
x > -2
Dr. B. is saving money to buy a new phone. He has already saved $400 and plans to save an additional $100 each week. He wants to have at least $1200 to buy the phone. How many weeks does he need to save money to reach his goal? Set up and solve your inequality. Write your answer in a sentence.
400 + 100w > 1200
w > 8 -- Dr. B has to save money for 8 weeks or more
z/30 > 70
z > 2,100
-9x + 1 > -71
x > -8
-3p + 1 < -11 OR p + 4 < 6
p > 4 OR p < 2
-5x - 5 > -3x - 4
x < -1/2
The school band is raising money for new instruments. They currently have $200 saved from previous fundraisers. Each month, they raise an additional $300 from their fundraising efforts. They want to have more than $800 to purchase the instruments. Solve an inequality that can be used to solve for the number of months, m, that the school band will need to raise enough money. Set up your inequality and write your answer in sentence form.
200 + 300m > 800
m > 2 -- They need to raise money for more than 2 months
-4x < 14
What is:
x > -7/2 OR x > -3.5
v < 48
8 < 4d + 12 < 32
-1 < d < 5
or
d > -1 and d < 5
2(-3x + 5) < 4
x > 1
A football team is planning a sports banquet. It costs $350 to rent the hall, and then $25 per person for the dinner. The committee needs to keep the total costs for the dinner under $1500. How many people can attend the dinner? Set up an inequality and write your answer in sentence form.
350 + 25p < 2500
p < 86 -- Less than 86 people can attend the dinner.
-58 > f - 9
Final answer must have variable on the left-hand side.
f < -49
11 < 2 - 3x
Final answer must have variable on the left-hand side.
x < -3
-12 < -3x + 6 < -6
6 > x > 4
or
x < 6 and x > 4
5 - 3(x + 2) < x + 5
x > -3/2
or
x > -1.5