10/28- Solving Two-Step and Multi-Step Inequalities

ID: tohon-jadam
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Avatar for Nicole SherrickNicole Sherrick, BP BY-NC
Subject: Algebra
Grade: 8
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17 questions

10/28- Solving Two-Step and Multi-Step Inequalities

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Two-Step Inequalities

1) 5f+7225f+7\leq22

2) 5y2<8-5y-2<8

3) 912+6r9\leq-12+6r

4) On a trip from Buffalo, New York, to St. Augustine, Florida, a family wants to travel at least 250 miles in the first 5 hours of driving. What should their average speed be in order to meet this goal?

Multi-Step Inequalities

5) 3(k5)+9k33(k-5)+9k\geq-3

6) 3(j+3)+9j<15-3(j+3)+9j<-15

7) 30>(5z+15)+10z30>-(5z+15)+10z

8) 4x+3<3x+64x+3<3x+6

9) 5f+82+6f5f+8\geq2+6f

10) 3m46m+113m-4\leq6m+11

Inequalities with Special Solutions

11) 3(w3)93w-3(w-3)\geq9-3w



a)

All Real Numbers

b)

No Solution

12) 2(6+s)152x-2(6+s)\geq-15-2x

a)

All real numbers

b)

No Solution

13) 2(n8)<16+2n2(n-8)<16+2n

a)

All Real Numbers

b)

No Solution

Mixed Inequalities
Solve each inequality, if possible. If the inequality has no solution, write 'no solution'; if the solutions are all real numbers, type 'all real numbers'.

14) 3(x3)54x-3(x-3)\geq5-4x

15) 3(2+t)152t3(2+t)\geq15-2t

16) 4(a2)6a94(a-2)-6a\leq-9

17) The student council wants to rent a ballroom for the 8th grade dance. The ballroom's rental rate is $1500 for 3 hours, and $125 for each additional half hour. Suppose the student council's budget is $2125. What is the maximum number of hours for which they can rent the ballroom?