Solving Inequality Models

Four times a number, increased by 6 is greater than 22.  Which inequality models this scenario?

• 4x - 6 > 22

• 4x + 6 < 22

• 4x + 6 ≥ 22

• 4x + 6 > 22

Does the sign need to flip when solving?
-2x ≥ 22

• YES

• NO

Solve
-5m < 10

• m < -2

• m > -2

• m < -50

• m > -50

Which is the solution of
-4 - 6m > -9m + 8?

• m < -4

• m > 4

• m < 15

• m > 36

Ms. Yaeger is going to Staples and can spend at most $156 on school supplies. She is buying binders that cost $5.64 and pencils that cost $1.27 per pack. Which of the following inequalities models her situation?

• 5.64x + 1.27y = 156

• 5.64x + 1.27y ≤ 156

• 5.64x + 1.27y ≥ 156

• 5.64x + 1.27y < 156

A carpenter has $60 with which to buy supplies. The carpenter needs to buy both nails and screws. Nails cost $12.99 per box, and screws cost $14.99 per box. If n represents the number of boxes of nails and s represents the number of boxes of screws, which of the following systems of inequalities models this situation?

• {12.99n+14.99s $\le$ 60
  
  {n $\ge$ 1
  
  {s $\ge$ 1

Anita is saving for college and wants to take no fewer than $3000 with her for the fall semester. Her summer job pays $9/hour. She has already saved $720. How many hours will Anita have to work during the rest of the summer to meet her goal? Select the inequality that models the situation if h represents the number of hours Anita will need to work.

Anita is saving for college and wants to take no fewer than $3000 with her for the fall semester. Her summer job pays $9/hour. She has already saved $720. How many hours will Anita have to work during the rest of the summer to meet her goal? Select the inequality that models the situation if h represents the number of hours Anita will need to work.

Garima likes her job as a baby-sitter (b), but it pays only Rs300 per hour. She has been offered a job as a tutor (t) that pays Rs600 per hour. Because of school, her parents only allow her to work a maximum of 15 hours per week, but she needs to make at least Rs6600 per week. Which system of inequalities below correctly models Joann's situation?

• b + t < 15

  3b + 6t > 66

• b + t > 15

  3b + 6t < 66

• 3b + 6t > 15

  b + t < 66

• 300b + 600t < 15

  b + t < 66

Kim wants to earn at least $65 from her two jobs next week. At most, she can work 15 hours. Her first job pays $5 per hour, and her second job pays $7 per hour. Let x represent the number of hours worked at the first job and y represent the number of hours worked at the second job. Which system of linear inequalities models Kim's situation?