Mixed Inequalities

Which point below is NOT part of the solution set?

• (0, 0)

• (5, 1)

• (-1, -3)

• (20, -5)

Cullin needs to save at least $100 for homecoming. He works 2 jobs earning $8/hour at Culvers and $25/hour mowing lawns. He only has time to work 14 hours before homecoming.

• x + y  ≥ 25
  x + y ≤ 8

• 100x + 25 y ≤ 100
  2x + 8y ≤ 14

• x + y ≥ 100
  8x + 25y ≤ 14

• 8x + 25y ≥ 100
  x + y ≤ 14

Solve:
3x + 2 < -7 or -4x + 5 < 1

• x < -3 and x < 1

• x < -3 and x > 1

• x < -3 or x < 1

• x < -3 or x > 1

When John bought his new computer, he purchased an online computer help service. The help service costs an initial $25.50 and a $10.50 charge is applied for each session a person uses. If John can only spend $170 for the computer help service, how many sessions can John use?

• x ≤ 13.76

• x ≤ 18.62

• x ≤ 6.25

• x ≤ 4.7

What is the solution to 2(b - 8) > 12?

• b > 20

• b > 6

• b > 14

• b < 20

A family swimming pool membership costs $45 per month plus a one time fee of $35. If a family can spend at most $395 on the pool membership, how many months can they be members?

• x ≤ 8

• x ≤ 10

• x ≥ 8

• x ≥ 10

Solve and graph the inequality −5x − 12 > −6x − 4

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Which graph shows the solution set to the inequality

−2(5y + 12) < −12y − 18

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Ms. Salgado needs to have her car repaired but does not want to spend more than $225 for the repairs. The mechanic says that the part needed for the repair will cost $78 and that labor will cost an additional $35 per hour. Which inequality below represents the greatest number of hours the mechanic can work without exceeding Ms. Salgado's budget?

• 78− 35x < 225

• 35 + 78x ≥ 225

• 35 + 78x ≤ 225

• 35x + 78 ≤ 225

Which is a solution of 5(v + 3) − 10v > −10

• v < 5

• v > 5

• v > −5

• v < −5