1. Bell Ringer 9/26/14
Test Questions

2. Objective The student will be able to:
graph inequalities on a number line.
solve inequalities using addition and subtraction.

3. 1) Graph the solution set of x < 3.
When you have < or >, use an open dot!

4. 2) Graph the solution set of y ≥ -5/4.•
When you have ≤ or ≥, use a closed dot! Converting -5/4 to a decimal = -1.25

5. 3) Graph the solution set of p ≠ 2.
When you have ≠, use an open dot and shade both ways!

6. 4) Which inequality would have a closed dot on the number line?
>
< ≥ ≠
Answer Now

7. 5) Which inequality does NOT use an open dot on the number line?≤
<
> ≠
Answer Now

8. o x - 14 < 16 + 14 + 14 x < 30 30 + (-14) = 16 16 = 16
6) Solve x + (-14) < 16
x - 14 < x < (-14) = = 16
Solve this problem like an equation
Draw “the river”
Eliminate double signs
Add 14 to both sides
Simplify
Check your answer
Graph the solution o 30 31 29

9. ● y ≥ - 14 (-14) + 21 = 7 7 = 7 7) Solve y + 21 ≥ 7 -14 -13 -15
y ≥ - 14
(-14) + 21 = 7
7 = 7
Draw the “river”
Subtract 21 from both sides
Simplify
Check your answer
Graph the solution
-14
-13
-15 ●

10. - 8y - 8y 3 > y - 14 + 14 + 14 17 > y y < 17 o
8) Solve y + 3 > 9y - 14
- 8y y
3 > y - 14
17 > y
y < 17
8(17) + 3 = 9(17) - 14
Draw “the river”
Subtract 8y from both sides
Simplify
Add 14 to both sides
Rewrite inequality with the variable first
Check your answer
Graph the solution o 17 18 16

11. ● ● o o 9) What is the graph of 7 ≤ m? 7 8 6 7 8 6 7 8 6 7 8 6
Answer Now

12. - 2r - 2r r – 17 ≥ 14 + 17 + 17 r ≥ 31 10) Solve 3r - 17 ≥ 2r + 14 ●
r ≥ 31
3(31) - 17 = 2(31) + 14
Draw “the river”
Subtract 2r from both sides
Simplify
Add 17 to both sides
Check your answer
Graph the solution ● 31 32 30

13. 11) Solve -2x + 6 ≥ 3x - 4
x ≥ -2
x ≤ -2
x ≥ 2
x ≤ 2
Answer Now

14. 12) Joanna’s tests were 87, 93, 88 and 94
12) Joanna’s tests were 87, 93, 88 and 94. What must her 5th grade be to get a total of at least 459? 96 97 98
100
Answer Now

15. Objective The student will be able to:
solve inequalities using multiplication and division.

16. 1) Which graph represents the correct answer to > 1-4 -3 -5 o -4 -3 -5 ● -4 -3 -5 ● -4 -3 -5
Answer Now

17. k < -52 o 1) Solve > 13 -52 -51 -53 Draw “the river”
Clear the fraction - Multiply both sides by -4
NEW STEP!! When multiplying BOTH sides by a NEGATIVE number, SWITCH the inequality!
Simplify
Check your answer
Graph the solution
k < -52 o
-52
-51
-53

18. 2) When solving > -10 will the inequality switch?
Yes!
No!
I still don’t know!
Answer Now

19. x < -30 2) Solve < -10 o -30 -29 -31 Draw “the river”
Clear the fraction - Multiply both sides by 3. Do you switch the inequality?
No - Both sides are being multiplied by a positive number
Simplify
Check your answer
Graph the solution
x < -30 o
-30
-29
-31

20. 3) When solving will the inequality switch?
Yes!
No!
I still don’t know!
Answer Now

21. a > -24 o 3) Solve -24 -23 -25 Draw “the river”
Clear the fraction - Multiply both sides by -4. Do you switch the inequality?
Yes - Both sides are being multiplied by a negative number
Simplify
Check your answer
Graph the solution
a > -24 o
-24
-23
-25

22. 4) Solve -8p ≥ -96
p ≥ 12
p ≥ -12
p ≤ 12
p ≤ -12
Answer Now

23. p ≤ 12 -8(12) = -96 ● 4) Solve -8p ≥ -96 12 13 11 Draw “the river”
Divide both sides by -8. Do you switch the inequality?
Yes - Both sides are being divided by a negative number
Simplify
Check your answer
Graph the solution
p ≤ 12
-8(12) = -96 ● 12 13 11

24. ● ● 5) Solve 7v < -105 o o -15 -14 -16 -15 -14 -16 -15 -14 -16 -15
Answer Now

25. Objective The student will be able to:
solve two-step inequalities.

26. 1) Solve 5m - 8 > 12
5m > 20
m > 4
5(4) – 8 = 12
Draw “the river”
Add 8 to both sides
Simplify
Divide both sides by 5
Check your answer
Graph the solution o 4 5 3

27. - 12 - 12 -3a > 6 -3 -3 a < -2 12 - 3(-2) = 18 o
2) Solve a > 18
-3a > 6
a < -2
12 - 3(-2) = 18
Draw “the river”
Subtract 12 from both sides
Simplify
Divide both sides by -3
Simplify (Switch the inequality!)
Check your answer
Graph the solution o -2 -1 -3

28. Which graph shows the solution to 2x - 10 ≥ 4?.
Answer Now

29. o -2m -2m 3m - 4 < 11 + 4 + 4 3m < 15 3 3 m < 5
3) Solve 5m - 4 < 2m + 11
-2m m
3m < 11
3m < 15
m < 5
5(5) – 4 = 2(5) + 11
Draw “the river”
Subtract 2m from both sides
Simplify
Add 4 to both sides
Divide both sides by 3
Check your answer
Graph the solution o 5 6 4

30. ● -2r -2r -18 ≤ 3r + 3 - 3 - 3 -21 ≤ 3r 3 3 -7 ≤ r or r ≥ -7
4) Solve 2r - 18 ≤ 5r + 3
-2r r
-18 ≤ 3r + 3
-21 ≤ 3r
-7 ≤ r or r ≥ -7
2(-7) – 18 = 5(-7) + 3
Draw “the river”
Subtract 2r from both sides
Simplify
Subtract 3 from both sides
Divide both sides by 3
Check your answer
Graph the solution ● -7 -6 -8

31. 6) Solve -2x + 6 ≥ 3x - 4
x ≥ -2
x ≤ -2
x ≥ 2
x ≤ 2
Answer Now

32. 5) Solve 26p - 20 > 14p + 64 o -14p -14p 12p – 20 > 64 + 20 + 20
12p > 84
p > 7
26(7) – 20 = 14(7) + 64
Draw “the river”
Subtract 14p from both sides
Simplify
Add 20 to both sides
Divide both sides by 12
Check your answer
Graph the solution o 7 8 6

33. What are the values of x if 3(x + 4) - 5(x - 1) < 5?
Answer Now

34. Objectives The student will be able to:
1. solve compound inequalities.
2. graph the solution sets of compound inequalities.

35. ● ● ● 1) Graph x < 4 and x ≥ 2 a) Graph x < 4 o o b) Graph x ≥ 23 4 2 o 3 4 2 o
b) Graph x ≥ 2 3 4 2 ● ●
c) Combine the graphs
d) Where do they intersect? ● 3 4 2 o

36. ● ● 2) Graph x < 2 or x ≥ 4 a) Graph x < 2 o o b) Graph x ≥ 43 4 2 o 3 4 2 o
b) Graph x ≥ 4 3 4 2 ● 3 4 2 ●
c) Combine the graphs

37. 3) Which inequalities describe the following graph?-2 -1 -3 o
y > -3 or y < -1
y > -3 and y < -1
y ≤ -3 or y ≥ -1
y ≥ -3 and y ≤ -1
Answer Now

38. 4) Graph the compound inequality 6 < m < 8
When written this way, it is the same thing as 6 < m AND m < 8 It can be rewritten as m > 6 and m < 8 and graphed as previously shown, however, it is easier to graph everything between 6 and 8! 7 8 6 o

39. 5) Which is equivalent to -3 < y < 5?
y > -3 or y < 5
y > -3 and y < 5
y < -3 or y > 5
y < -3 and y > 5
Answer Now

40. 6) Which is equivalent to x > -5 and x ≤ 1?
Answer Now

41. ● ● 7) 2x < -6 and 3x ≥ 12 o o o o -3 -6 -3 -6 4 7 1 4 7 1
Solve each inequality for x
Graph each inequality
Combine the graphs
Where do they intersect?
They do not! x cannot be greater than or equal to 4 and less than -3 No Solution!! -3 -6 o -3 -6 o 4 7 1 o ● 4 7 1 o ●

42. Remember, when written like this, it is an AND problem!
8) Graph 3 < 2m – 1 < 9
Remember, when written like this, it is an AND problem!
3 < 2m – 1 AND 2m – 1 < 9
Solve each inequality.
Graph the intersection of 2 < m and m < 5. 5 -

43. 9) Graph x < 2 or x ≥ 4 5 -

44. The whole line is shaded!!
10) Graph x ≥ -1 or x ≤ 3
The whole line is shaded!!