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

17 questions

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

##### Two-Step Inequalities

1) $5f+7\leq22$

2) $-5y-2<8$

3) $9\leq-12+6r$

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) $3(k-5)+9k\geq-3$

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

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

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

9) $5f+8\geq2+6f$

10) $3m-4\leq6m+11$

##### Inequalities with Special Solutions

11) $-3(w-3)\geq9-3w$

All Real Numbers

No Solution

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

All real numbers

No Solution

13) $2(n-8)<16+2n$

All Real Numbers

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) $-3(x-3)\geq5-4x$

15) $3(2+t)\geq15-2t$

16) $4(a-2)-6a\leq-9$

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?