Transcript x + 2 - Miami Beach Senior High School

Name:
Date:
Period:
Topic: Solving Inequalities
Essential Question: What is the correlation between solving equations
and solving inequalities?
Warm-up:
Name the following inequality signs:
Inequality Symbols
    
Less
than
Less
than or
equal to
Greater than
Not
equal to
Greater than
or equal to
Vocabulary:
An inequality is like an equation,
but instead of an equal sign (=) it
has one of these signs:
Solving the Inequality
w+5<8
Note:
We will use the same steps that we did
with equations, if a number is added to
the variable, we subtract the same
number to both sides.
Answer
w+5<8
w + 5 -5 < 8 -5
w+0<3
w<3
All numbers less
than 3 are
solutions to this
problem!
Now you try it!
7>x–5
8 + r ≥ -2
x - 2 > -2
4+y≤1
x+2≤3
Answers to Practice Problems:
8 + r ≥ -2
8 -8 + r ≥ -2 -8
r + 0 ≥ -10
w ≥ -10
All numbers from -10 and
up (including
-10) make this problem
true!
x - 2 > -2
4+y≤1
x - 2 + 2 > -2 + 2 4 - 4 + y ≤ 1 - 4
x+0>0
x>0
All numbers greater than 0
make this problem true!
y + 0 ≤ -3
y ≤ -3
All numbers from -3
down (including -3)
make this problem
true!
Answers to Practice Problems:
x+2≤3
x-5>7
x+2-2≤7-2
x–5+5>7+5
x+0≤5
x + 0 > 12
x≤5
x > 12
0
12
0
5
What do these means?
x<5
x>4
x≤3
x≥2
How to graph the solutions
> Graph any number greater than. . .
x>4
open circle, line to the right
< Graph any number less than. . .
open circle, line to the left
x<5
 Graph any number greater than or equal to. . .
closed circle, line to the right
x≥2
 Graph any number less than or equal to. . .
closed circle, line to the left
x≤3
Solving the Inequality
<-2
15b < 60
Answers
x>4
x<-8
<-2
15b < 60
15b < 60
15 15
b<4
That was easy!!!
But wait there is one special case:
● Sometimes you may have to reverse the
direction of the inequality sign!!
● That only happens when you multiply or
divide both sides of the inequality by a
negative number.
Solving the Inequality
- 4r > 16
Answers
(
- 4r > 16
(
- 4r > 16
-4
-4
(
(
r<-4
m < - 10
Solving multi-step inequalities
is like
solving multi-step equations.
If you can solve
2 x  3  11
you can solve
2 x  3  11
2 x  3  11
Remember:
2 x  3  11
Which graph shows the solution to
2x - 10 ≥ 4?
Now you try it!
Page 181 (1 – 4, 8, 16, 20)
1)
2)
3)
4)
5)
3(x + 4) - 5(x - 1) < 5
-2x + 6 ≥ 3x – 4
3 (t + 1) – 4t ≥ - 5
5m - 8 > 12
-5x – 9 < 26
Anytime you multiply or
divide both sides of an
inequality by a negative
number, you need to
reverse the sign.
Wrap-Up:
Brief Review of Inequalities
• Add/subtract the same number on each side of an inequality
• Multiply/divide by the same positive number on each side of an
inequality
• If you multiply or divide by a negative number, you MUST flip the
inequality sign!
Home-Learning:
Page 175 (34), Page 176 (70),
Page 181 (12, 21, 24), Page 189 (2, 4),
Page 190 (20), Page 192 (59, 60)