# 7-3 Solving Multi-Step Inequalities

```Warm ups – solve and graph
1.
2.
3.
4.
5.
6.
a + 4 &gt; 16
1. a &gt; 12
15 &lt; x – 3
2. x &gt; 18
.5
3. p &gt; -28
p  20
7
4. v &gt; 12
-9v &lt; -108
5. x &lt; -16
208 &lt; -13x
The sum of x and 3 is at least 7.
7-3 Solving Multi-Step
Inequalities
Objective: To solve inequalities
involving more than one
operation
2 Times you flip the inequality
1.
2.
Move variable to the left
Multiply or divide by a negative number
Example 1- watch
2 – work with me 
Solve the inequalities the SAME WAY you solved equations.
5(n  2)  4(n  6)
5(k  4)  2(k  6)  5(k  1)  1
Example 3
(3) x &lt; 2x – 15 (3)
3
3x &lt; 2x – 15
-2x -2x
x &lt; -15
TOO
1.
-3 &gt; -3t + 6
2.
26p – 20 &gt; 14p + 64
3.
. t  3  8
2
1. t &gt; 3
2. p &gt; 7
3. t &lt; -19
Special Case #1
3x + 4 &gt; 2(x + 3) + x
3x + 4 &gt; 2x + 6 + x
3x + 4 &gt; 3x + 6
-3x
-3x
4&gt;6
• Distribute
•Combine like terms
•Get variable on
same side
•True or false?
This state is FALSE:
No Solution
Special Case #2
3 – 3(y – 2) &lt; 13 – 3(y – 6) • Distribute
3 – 3y + 6 &lt; 13 – 3y + 18 •Combine like terms
•Get variable on
-3y + 9 &lt; -3y + 31
same side
+3y
+ 3y
•True or false?
9 &lt; 31
This state is TRUE:
All Numbers
Define a variable, write an
inequality, and solve.
The sum of two consecutive even integers is greater
than seventy-five. Name 2 consecutive even
integers that meet the requirement.
38, 40
40, 42
42, 44
Homework


Pg. 402 #17-41 ODD
Quiz Tomorrow!
GAME TIME!

Snake…



Whiteboard, sock, marker.
Pack up everything
Sit quietly.
Solve each inequality.
3  3t  6
t 3
2
w3 7
3
w  15
8n  2  10n  20
n  9
Solve each inequality.
5  4m  8  2m  17
2 x  15
x
3
m  15
x  15
6 p  2  4 p  12
p7
Solve each inequality.
3( x  2)  8 x  44
x  10
5(k  4)  3(k  4)
k  1
```