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

ID: tohon-jadam
Nicole Sherrick, BP BY-NC
Subject: Algebra
Grade: 8
PreviewAnswer Key

17 questions

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

Classroom:
Due:
Student Name:
Date Submitted:
##### 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) ﻿﻿$-3(w-3)\geq9-3w$﻿

a)

All Real Numbers

b)

No Solution

12) ﻿$-2(6+s)\geq-15-2x$﻿

a)

All real numbers

b)

No Solution

13) ﻿$2(n-8)<16+2n$﻿

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) ﻿$-3(x-3)\geq5-4x$﻿

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?