Download Solving Inequalities with Addition and Subtraction

Lesson 38 Solving Linear
Inequalities
NCSCOS Obj.: 1.01; 4.01
Daily Objectives
TLW graph inequalities on a number line.
TLW solve inequalities using addition,
subtraction, multiplication and division
TLW solve multi-step inequalities
1) Graph the solution set of
x < 3.
o
-5
0
5
When you have < or >, use an open dot!
2) Graph the solution set of
y ≥ -5/4.
-5
•
0
5
When you have ≤ or ≥, use a closed dot!
Converting -5/4 to a decimal = -1.25
3) Graph the solution set of
p ≠ 2.
-5
0
o
5
When you have ≠, use an open dot and shade
both ways!
4) Which inequality would have a
closed dot on the number line?
1.
2.
3.
4.
>
<
≥
≠
Answer Now
5) Which inequality does NOT use an
open dot on the number line?
1.
2.
3.
4.
≤
<
>
≠
Answer Now
6) Solve x + (-14) < 16
x - 14 < 16
+ 14 + 14
x < 30
Solve this problem like
an equation
1. Draw “the river”
2. Eliminate double
signs
3. Add 14 to both sides
4. Simplify
5. Check your answer
6. Graph the solution
29
30 + (-14) = 16
16 = 16
o
30
31
1.
2.
7) Solve y + 21 ≥ 7
- 21 -21
Draw the “river”
Subtract 21 from
y
≥
-14
both sides
3. Simplify
4. Check your answer
5. Graph the solution
-15
30 + (-14) = 16
16 = 16
●
-14
-13
8) Solve
1.
2.
3.
4.
5.
6.
7.
8.
Draw “the river”
Subtract 8y from both
sides
Simplify
Add 14 to both sides
Simplify
Rewrite inequality
with the variable first
Check your answer
Graph the solution
16
8y + 3 > 9y - 14
- 8y
- 8y
3 > y - 14
+ 14 + 14
17 > y
y < 17
8(17) + 3 = 9(17) - 14
o
17
18
9) What is the graph of 7 ≤ m?
1.
2.
3.
4.
6
6
6
6
o
7
o
7
●
7
●
7
Answer Now
8
8
8
8
10) Solve
1.
2.
3.
4.
5.
6.
7.
Draw “the river”
Subtract 2r from both
sides
Simplify
Add 17 to both sides
Simplify
Check your answer
Graph the solution
30
3r - 17 ≥ 2r + 14
- 2r
- 2r
r – 17 ≥ 14
+ 17 + 17
r ≥ 31
3(31) - 17 = 2(31) + 14
●
31
32
11) Solve -2x + 6 ≥ 3x - 4
1.
2.
3.
4.
x≥
x≤
x≥
x≤
-2
-2
2
2
Answer Now
12) Joanna’s tests were 87, 93, 88
and 94. What must her 5th grade be
to get a total of at least 459?
1.
2.
3.
4.
96
97
98
100
Answer Now
1) Which graph represents the
k
correct answer to
>1
4
1.
2.
3.
4.
-5
-5
-5
-5
o
-4
o
-4
●
-4
●
-4
Answer Now
-3
-3
-3
-3
1) Solve
1.
2.
3.
4.
5.
6.
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
-53
4
k
>
13
4
k

13 -4
4
k < -52
52
 13
4
o
-52
-51
x
When solving 3 > -10
will the inequality switch?
1. Yes!
2. No!
3. I still don’t
know!
Answer Now
1.
2.
x
2) Solve
< -10
3
Draw “the river”
x
Clear the fraction 3
 10 3
Multiply both sides by 3.
3
Do you switch the
inequality?
x < -30
30
 10
3
No - Both sides are being
multiplied by a positive
number
3.
4.
5.
Simplify
Check your answer
Graph the solution
-31
o
-30
-29
a
6
3) When solving
4
will the inequality switch?
1. Yes!
2. No!
3. I still don’t
know!
Answer Now
1.
2.
a
6
3) Solve
4
Draw “the river”
a
Clear the fraction -4
 6 -4
Multiply both sides by -4.
4
Do you switch the
inequality?
x > -24
Yes - Both sides are being
multiplied by a negative
number
3.
4.
5.
(24)
6
4
Simplify
Check your answer
Graph the solution
-25
o
-24
-23
4) Solve -8p ≥ -96
1.
2.
3.
4.
p ≥ 12
p ≥ -12
p ≤ 12
p ≤ -12
Answer Now
-8p ≥ -96
8 p 96

8
8
p ≤ 12
-8(12) = -96
4) Solve
1.
2.
Draw “the river”
Divide both sides by -8.
Do you switch the
inequality?
Yes - Both sides are being divided
by a negative number
3.
4.
5.
Simplify
Check your answer
Graph the solution
11
●
12
13
5) Solve 7v < -105
1.
2.
3.
4.
o
-16 -15 -14
o
-16 -15 -14
●
-16 -15
●
-14
-15 -15 -14
Answer Now
1.
2.
3.
4.
5.
6.
7.
1) Solve 5m - 8 > 12
Draw “the river”
+8 +8
Add 8 to both sides
5m
> 20
Simplify
Divide both sides by 5
5
5
Simplify
Check your answer
m>4
Graph the solution
5(4) – 8 = 12
3
o
4
5
1.
2.
3.
4.
5.
2) Solve 12 - 3a > 18
Draw “the river”
- 12
- 12
Subtract 12 from both
-3a > 6
sides
Simplify
-3 -3
Divide both sides by -3
Simplify
a
<
-2
(Switch the inequality!)
Check your answer
12 - 3(-2) = 18
6.
7. Graph the solution
-3
o
-2
-1
Which graph shows the solution to
2x - 10 ≥ 4?
1.
.
2.
3.
4.
Answer Now
3) Solve 5m - 4 < 2m + 11
1. Draw “the river”
2. Subtract 2m from both
sides
3. Simplify
4. Add 4 to both sides
5. Simplify
6. Divide both sides by 3
7. Simplify
8. Check your answer
9. Graph the solution
4
-2m
-2m
3m - 4 < 11
+4 +4
3m < 15
3
3
m<5
5(5) – 4 = 2(5) + 11
o
5
6
4) Solve 2r - 18 ≤ 5r + 3
1.
2.
3.
4.
5.
6.
7.
8.
9.
Draw “the river”
Subtract 2r from both sides
Simplify
Subtract 3 from both sides
Simplify
Divide both sides by 3
Simplify
Check your answer
Graph the solution
-8
-2r
-2r
-18 ≤ 3r + 3
-3
-3
-21 ≤ 3r
3
3
-7 ≤ r or r ≥ -7
2(-7) – 18 = 5(-7) + 3
●
-7
-6
6) Solve -2x + 6 ≥ 3x - 4
1.
2.
3.
4.
x≥
x≤
x≥
x≤
-2
-2
2
2
Answer Now
5) Solve
1.
2.
3.
4.
5.
6.
7.
8.
9.
Draw “the river”
Subtract 14p from both
sides
Simplify
Add 20 to both sides
Simplify
Divide both sides by 12
Simplify
Check your answer
Graph the solution
6
26p - 20 > 14p + 64
-14p
-14p
12p – 20 > 64
+ 20 + 20
12p > 84
12
12
p>7
26(7) – 20 = 14(7) + 64
o
7
8
What are the values of x if
3(x + 4) - 5(x - 1) < 5?
1.
2.
3.
4.
x < -6
x > -6
x<6
x>6
Answer Now