Transcript An inequality.

By the end of today: I will
know what an inequality is.
January 18, 2012
An equation.
• Solve this and graph the answer on a number line:
x-2 = 5
What does x = 7 MEAN?
An inequality.
• Consider this example:
x–2>5
What does it mean?
What numbers minus two are greater than 5?
Well…there are several. Any number bigger than 7.
So we write our answer with an inequality. Usually
we are asked to graph our solution as well.
To graph an inequality with one
variable…
• Find all of the possible solutions (solve).
• Draw a number line.
– You do not have to put all of the numbers.
– You DO need to put a 0 in the middle and the
number from the solution.
• Where you put the number, you have two options:
– open circle o for < and >
– closed circle • for ≤ and ≥
• Then shade in the direction of the possible solutions.
Solving Inequalities with
Addition and Subtraction
• My turn
• Your turn
1.
2.
y–2<6
y–7<4
Solving Inequalities with
Addition and Subtraction
• My turn
• Your turn
3.
4.
t + 12 ≥ -26
m + 7 ≥ -14
Solving Inequalities with
Multiplication and Division
• Multiplication and Division are exactly what
you think they are with one exception:
– ANY time you multiply BOTH sides or divide
BOTH sides by a negative number, you must flip
the sign.
• Why?
Why do we change the sign when we
multiply or divide BOTH sides by a negative?
• Algebraically:
x<y
0<y–x
-y < -x
• Or think of it as a number
line:
0
x y
x<y
• When we multiply by -1, we
are reflecting across the
zero, so…
-x > - y
-y -x 0
-x > -y
Solving Inequalities with
Multiplication and Division
• My turn
• Your turn
7.
8.
2s < 42
3h > 45
Solving Inequalities with
Multiplication and Division
• My turn
• Your turn
9.
10.
–8p > -32
–4d < -12
Solving Inequalities with
Multiplication and Division
• My turn
• Your turn
11.
12.
9k < 17
6b ≤ 31
Solving Inequalities with
Multiplication and Division
• My turn
13.
k > -2
4
• Your turn
14. m > -6
2
Solving Inequalities with
Multiplication and Division
• My turn
15.
r > -3
9
• Your turn
16. x < 2.6
5
Solving Inequalities with
Multiplication and Division
• My turn
• Your turn
17. 1 c ≥ 0
5
18. 2 d ≤ -3
3
Homework
Worksheet
Quiz next time over this.