Download Solving Inequalities: Part 2

Solving Inequalities: Part 2
Chapter 4.6
Multiplying and Dividing in
Inequalities:
If you multiply or divide both sides by a
negative number, then you must reverse
the inequality sign.
Solve:
–4x < 12
Divide by NEGATIVE 4
4 x 12

4 4
x > -3
Change the “less than” sign to
“greater than.”
Why reverse the inequality sign?
–4x < 12
x < -3
Suppose we didn’t
reverse our sign.
x is less than –3.
Try examples
-4(-5) < 12
20 < 12,
20 is NOT less than 12.
-4(-10) < 12
40 < 12
40 is NOT less than 12.
Fractions:
Solve and graph your solution on a number line:
2
8 y
3
Multiply by the
reciprocal.
 3
 3 2
  8      y
 2
 2 3
12  y
Because we are multiplying
by a negative, we reverse
the sign.
Graph the Inequality:
12  y
We use a closed circle.
Negative 12 is greater
than or equal to y.
-14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3
-2 -1 0
If you don’t know which way the arrow should
go, try plugging in a number and seeing if it
makes a true statement.
Other Examples: Try to solve in notebook.
x
  100
4
We are dividing x by a
negative 4. So, we must
multiply both sides by
negative 4.
x
 4   100  4
4
x  400
Don’t forget to switch
the inequality sign!
Graphing Inequalities:
You choose the scale.
x  400
If you have very large, or very small numbers,
remember that you can choose how you
label your number line.
-600
-500
-400
-300
-200
-100
x is less than or equal to –400,
so x could be –500 or –600.
0
Fractions and Inequalities
5  1 p
6
3
The variable is multiplied
by negative 1 .
3
 3  5  3  1 So we must multiply both
        p sides by the reciprocal.
 16  1 3
15
 p
6
Don’t forget to
switch the
inequality sign!
Graphing Fractions and
Mixed Numbers
On a number line: Turn any improper fractions
into mixed numbers.
1
2  p
2
15
1
  2
6
2
-4
-3
-2
-1
0
Homework: Page 188-189
(17-43 odds)
SHOW WORK.
Solution on numberline!