6.2 Solving Inequalities
with Mult. and Div.
solve inequalities using multiplication and
division.
PFA 7 and 9
Designed by Skip Tyler, Varina High School
Edited by Eddie Judd, Crestwood Middle School
Edited by Dave Wesley, Crestwood Middle School
Investigate
• If 5 > 2, can I multiply each side by 10 and
keep the inequality true?
• If 5 > 2, can I multiply each side by -10 and
keep the inequality true?
Investigate
• If 4 < 12, can I divide each side by 2 and
keep the inequality true?
• If 4 < 12, can I divide each side by -2 and
keep the inequality true?
What do we know?
• Multiply or divide by a ____________
will not affect the inequality.
Sign ________
• Multiply or divide by a ____________
will affect the inequality.
Sign ________
Let’s look at this idea again!
• What if my original inequality contains a
negative value? (multiply)
• For example:
-5 < 10
Conclusion
• What if my original inequality contains a
negative value? (divide)
• For example:
• Do I still agree?
8 > -2
YES !
x
1) When solving
> -10
3
will the inequality switch?
1. Yes!
2. No!
3. I still don’t
know!
Answer Now
1.
2.
x
1) Solve
< -10
3
Draw “the river”
Clear the fraction Multiply both sides by 3.
Do you switch the
inequality?
3
{x | x < -30}
30
 10
3
No - Both sides are being
multiplied by a positive
number
3.
4.
5.
x
 10 3
3
Simplify
Check your answer
Graph the solution
-31
o
-30
-29
2) 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
2) 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 | k < -52}
52
 13
4
o
-52
-51
 1a
6
4
3) When solving
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 | 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
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?
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 | 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
Assignment
• Page 305 13-33 odds and 46-49 all