1. Solving Inequalities

2. Objective 3.2 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 3.3 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. 2) Solve < -10 x < -30 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. Take a quick break!
Things that make you go.....Hmmm Why is abbreviation such a long word? Why do they have braille dots on the ATM machines in drive-thru’s?

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

24. 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

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