Transcript Chapter 7 Lesson 4 Solving Inequalities by Adding or

Chapter 7 Lesson 4
Solving Inequalities by
Adding or Subtracting
pgs. 345-349
What you’ll learn:
Solve inequalities by using the
Addition or Subtraction
Properties of Inequality
 Solving an inequality means finding
values for the variable that make the
inequality true.
You can solve inequalities by using the
Addition and Subtraction Properties of
Inequalities (pg. 345) This is the same
concept as using the
Addition/Subtraction Properties of
Equations (Lesson 3-3 pgs. 110-111)
Example 1: Solving an Inequality
using Subtraction
Solve -13  9 + b
Write the inequality:
Check your solution
-13  9 + b
Subtract 9 from each side: -13  9 + b
-9 -9
Simplify: -22  b or b  -22
To check your solution, try any number less than or equal
to -22
Check using -20:
Check:
using
-30
Check using -22:
-13  9 + -20
-13  9 + -30
-13  9 + (-22)
-13  -11
-13

-21
-13  -13 
Example 2: Solving an Inequality
using Addition
Solve a - 5  6
Check your solution
Write the inequality: a - 5  6
Add 5 to both sides: a - 5  6
+5 +5
Simplify: a  11
Check your result by using any number greater than 11
Check using 12:
12 - 5  6
76
Check using 32:
32 - 5 6
27  6 
Check using 7:
7-56
26
Example 3: Graph Solutions of
Inequalities
Solve h + 4  4 Then graph the
solution on a number line.
Write the inequality: h + 4  4
Subtract 4 from each side: h + 4  0
- 4 -4
h0
The solution is h  0
Check: any number greater than 0
I’m using 1
1+44
54
Now graph the solution
On a number line.
Done on board in class.
Example 4: Use an Inequality to
Solve a Problem
Chris is saving money for a ski trip. He has
$62.50, but his goal is to save at least
$100. What is the least amount Chris
needs to save to reach his goal?
Explore: We need to find the least amount Chris needs to save
Plan: Let x represent the amount he needs to save. Write
an inequality to represent the problem. Remember
at least means greater than or equal to.
x + 62.50  100
Solve: x + 62.50  100
- 62.50 -62.50
x  37.50
So the least amount that Chris
needs to save is $37.50
Your Turn! Solve the inequality,
graph your solution, do a check
A. c - (-2)  3
B.
c+23
-2 -2
c1
Check using -1
-1 - (-2)  3
13
25  n + (-12)
+12
25  n + (-12) +12
37 < n , n  37
Check using 40
25  40 + (-12)
25  28
g - 5 + 5  13 + 5
Check using 4
3
6
3 3 6
3
4 - 12  2 1
3
6
g3 5
1
1
6
2 2 
6
k + 9  -21 Check using -25 3
D. k + 9  -21
- 9 -9
-25 + 9  -30
k  -30
-16  -30 
C. g - 1 2  2 1
Extra Practice by the door on your
way out. See me if you have
questions/problems!