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# 6.2 Solving Inequalities

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## Tina Lee

on 23 July 2015

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#### Transcript of 6.2 Solving Inequalities

Practice: Solving Inequalities
Example 2
Example 3
Practice Time! Try Both Kinds!
6.2 Solving Inequalities
Solving Inequalities
WHAT
: Solving inequalities for the unknown variable
Keypoints
Solving inequalities is the
same as
solving
equations
except...
Example 1
Two Step Inequalities!
Because you know how to solve equations, this will just take practice! *Remember to flip the sign when multiplying or dividing by a negative number.
Multi-Step Equations
Alright, AGAIN! You've seen these problems before! Just do what you do best, and remember the rules regarding the inequality symbol! :)
HOW
: Isolate the variable to one side of the inequality using inverse operations
ONE DIFFERENCE
:
When multiplying or dividing by a negative number, switch the direction of the sign/inequality symbol
This should be easy enough!
It's just like solving equations! :]
Adding and Subtracting- One Step Equations
Example 1:
17 + k 10
subtract 17 on both sides
17 + k 10
-17
-17
k -7
Graph:
k -7
k is less than or equal to (filled in circle)
less than = arrow to the left
x - 1
3
x - 1
3
+1
+1
x 4
-18 + n < -7
-18 + n < -7
+18
+18
n < 11
*
Remember
: When multiplying or dividing by a
negative
number,
flip the sign
.
17. 24 -4n
divide by -4 on each side
-4
-4
divided by negative
switch the sign
-6
n
-6
n
or n
-6
Solve and graph
Did you get the right answer? Check here!
m
5
3
multiply by 3 on both sides
m
15
multiplied by positive number
sign stays the same
n > -13

p

3
k -7
*Try NOT flipping the sign to see why we must!
-11 x - 4 > -15
step 1: add 4 on both sides
+4
+4
-11x > -11
step 2: divide by -11 on both sides
-11
-11
*since I divided by a negative, switch the sign
x >
-1

x
<

-1

*open circle
*less than- to the left
#9. 1. subtract 5 on both sides
2. Divide by -7 on both sides
3. Switch the sign (divided by a negative) and graph
1. Multiply by 2 on both sides
2. Subtract by 3 on both sides
1. Multiply by 2 on both sides
2. Subtract 1 on both sides
#12. 1. Add 2 on both sides
2. Times by 2 on both sides
Multi-step:
1. Use the distributive property.
1. -3p - (-21)
21
2. Add the opposite (leave, change, change)
2. -3p + (+21)
21
3. -3p + 21
21
3. Subtract 21 from each side.
-21
-21
-3p
0
4. Divide by -3 on both sides/ change the direction of the sign.
p
0
Multi-step Inequalities Practice Problems
Make sure to show your work!
1. Combine like terms on both sides of the inequality
-6x - 16 < 2x
2. Bring all x terms to one side- Add 6x on both sides
- 16 < 8x
3. Divide each side by 8
-2 < x or x > -2
1. Combine like term on both sides.
-7 -6x > -11 -7x
2. Bring all x terms to one side-
Add 7 x to both sides
-7 + x > - 11
3. Add 7 to both sides
x > -4
#10.
#11.
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