1. Solving Inequalities
Algebra 1

2. Solving inequalities is similar to solving linear equations (ex
Solving inequalities is similar to solving linear equations (ex. 2x+2=4), except for one small but important detail: you flip the inequality sign whenever you multiply or divide the inequality by a negative number.
Examples
-2x=4, answer: x=-2
-2x≥4, answer: x≤-2

3. Remember: ~The opposite of addition is subtraction
~The opposite of subtraction is addition
~The opposite of multiplication is division
~The opposite of division is multiplication
~When multiplying or dividing by a negative number,
the sign of the inequality switches

4. Please complete the following questions for homework tomorrow.

5. Solve.
m - 3 < 6

6. Answer: m<9 ~add 3 to both sides

7. Solve.
3 + a < 6

8. Answer: a<3 ~subtract 3 from both sides

9. Solve.
-2 > x - 3

10. Answer: x<1
~add 3 to both sides

11. Solve.
t + (-3) > -4

12. Answer: t >-1
~Add 3 to both sides

13. Solve.
3 + y < -2

14. Answer: y<-5
~Subtract 3 from both sides

15. Solve.
2x < -8

16. Answer: t<-4
~Divide 2 from each side

17. Solve.
12 > 6k

18. Answer: k<2
~Divide by 6 on both sides

19. Solve.

20. Answer: a>6 ~Multiply by -3 on both sides, flip the inequality sign

21. Simplify.

22. Answer: a>-10 ~Multiply each side by 5, then divide each side by 2

23. Solve.

24. Answer: a<-9 ~Multiply each side by 3, then divide each side by -2, switch the inequality sign because we are dividing by a negative number

25. Solve.
3x - 1 > 5

26. Answer: x>2 ~Subtract 1 from each side, then divide each side by 3

27. Solve.
-2n + 3 < 7

28. Answer: n>-2 Subtract 3 from each side then divide each side by a -2, switch the inequality sign because we are dividing by a negative number

29. Solve.
8 < 2 - 3r

30. Answer: r<-2 ~Subtract 2 from each side then divide by -3, switch the inequality sign because we are dividing by a negative number

31. Solve.

32. Answer: x<-3 ~Subtract 1 from each side, then multiply each side by -3, switch the inequality sign because we are multiplying by a negative number

33. Solve.

34. Answer: x<-7 Multiply each side by 5, then subtract 2 from each side

35. Write an inequality:
A number is greater
than -3.

36. Answer: n<-3

37. Write an inequality:
2 less than a number
is less than 9.

38. Answer: n-2<9

39. Helpful Websites http://www.youtube.com/watch?v=VgDe_D8ojxw

40. SOL Regulations
A.5 The student will solve multistep linear inequalities in two variables, including
a) solving multistep linear inequalities algebraically and graphically;
b) justifying steps used in solving inequalities, using axioms of inequality and
properties of order that are valid for the set of real numbers and its subsets;
c) solving real-world problems involving inequalities; and
d) solving systems of inequalities.