Mild Inequalities
Solve this inequality: 3<-5n+2n
What is: n<-1
Solve this inequality: -3-6(4x+6)>-111
What is x<3
n<2 represents all possible solutions of: -6n<-12
What is false. n>2 represents all possible solutions.
The price of a train ticket consists of an initial fee of $5, plus a fee of $2.75 per stop. Julia has $21 and would like to travel 50 miles. She wants to know the largest number of stops she can afford to buy on a ticket.
Let S represent the number of stops that Julia buys.
5+2.75⋅S≤21
How many stops can Julia afford?
What is 5 stops
Solve this inequality: 6x+2+6x<14
What is x<1
Solve this inequality: 6-4(6n+7)≥122
What is n≤-6
Look at the following problem. In which step is a mistake made?
Problem: −4(6 − y) + 4 = −4
Step 1: −24 − 4y + 4 = −4
Step 2: −20 − 4y = −4
Step 3: −4y = 16
Step 4: y = −4
What is step 1.
Rebekah manages a yoga studio that charges each customer a one-time initial fee of $35, and an additional fee of $12, per class taken. Rebekah's goal is for each customer to spend at least $100, at the studio, and she wants to know the minimum number of classes a customer needs to take to meet that goal.
Let C represent the number of classes a customer takes.
35+12C≥100
What is the minimum number of classes a customer can take for Rebekah to meet her goal?
What is 6 classes
Solve this inequality: -p-4p>-10
What is p<2
Solve the inequality: -138≥-6(6b-7)
What is b≥5
Which of the following is not a solution of this equation: 3x(x-1)(x-2)=0
a.0
b.1
c.2
d.3
What is 3
Jackie needs to buy some pizzas for a party at her office. She's ordering from a restaurant that charges a $7.50 delivery fee and $14 per pizza. She wants to buy as many pizzas as she can, and she also needs to keep the delivery fee plus the cost of the pizzas under $60.
Each pizza is cut into 8 slices, and she wonders how many total slices she can afford.
Let P represent the number of pizzas that Jackie buys.
Write an inequality that describes this situation.
What is 7.50+14P<60
Solve this inequality: 18≥5k+4k
What is k≤2
Solve the inequality: 167<6+7(2-7r)
What is r<-3
Emily is solving the equation 2(x + 9) = 4(x + 7) + 2. Her steps are shown below.
Step 1: 2(x+9)=4(x+7)+2
Step 2: 2x+18=4x+28+2
Step 3: 2x+18=4x+26
Step 4: -8=2x
Step 5: -4=x
What step did she make a mistake in AND what is the correct solution to the problem?
What is Step 3 AND -6.
Nancy needs at least 1000 gigabytes of storage to take pictures and videos on her upcoming vacation. She checks and finds that she has 105 GB available on her phone. She plans on buying additional memory cards to get the rest of the storage she needs.
The cheapest memory cards she can find each hold 256 GB and cost $10. She wants to spend as little money as possible and still get the storage she needs.
Let C represent the number of memory cards that Nancy buys.
Write an inequality that describes this scenario.
What is 105+256C≥1000
Solve this inequality: 9≥-2m+2-3
What is m≥-5
Solve the inequality: 5(6+3r)+7≥127
What is r≥6
Look at this linear equation: y=2/5x+2
What is the value of x when y=2 2/3
1 2/3
Nina has some money saved for a vacation she has planned.
• The vacation will cost a total of $1600.
• She will put $150 every week into her account to help pay for the vacation.
• She will have enough money for the vacation in 8 weeks.
If Nina was able to save $200 a week instead of $150 a week, how many fewer weeks would it take her to save enough money for the vacation? Write the result below.
What is 2 weeks