Download graph of an inequality

Do Now 3/6/14
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Take out HW from last night.
– Practice worksheet 11.4 B
Copy HW in your planner.
– Text p. 490, #8-34 evens, 43 & 44
Complete Practice worksheet 11.4 C
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On a number line, the GRAPH OF AN
INEQUALITY is the set of points that
represent the SOLUTION SET of the
inequality.
“Less than” and “greater
than” are represented
with an open circle.
x<8
5
6
“Less than or equal to”
and “greater than or equal
to” are represented with a
closed circle.
8
9
7
8
9
10
x ≥ 11
10
11
12
13
14
11
Graph each inequality
7≥y
“Less than or equal to”
and “greater than or equal
to” are represented with a
closed circle.
4
5
6
7
8
9
“Less than” and “greater
than” are represented
with an open circle.
-1 < h
-4
-3
-2
-1
10
0
1
2
COMPOUND INEQUALITY
–
consists of two separate inequalities
joined by AND or OR.
“AND”
Compound Inequalities
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The graph of a compound inequality with AND is the
INTERSECTION of the graphs of the inequalities.
Graph x > -2
-2
-1
0
1
2
3
2
3
Graph x ≤ 1
-2
-1
0
1
Graph -2< x ≤ 1
Graph of x ≤ 1 and x > -2
-2
-1
0
1
2
3
“OR”
Compound Inequalities
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The graph of a compound inequality with OR is the
UNION of the graphs of the inequalities.
Graph x > 2
-2
-1
0
1
2
3
2
3
Graph x ≤ -1
-2
-1
0
1
Graph of x ≤ -1 or x > 2
-2
-1
0
1
2
3
Graph each compound inequality
5<y≤9
4
5
6
7
8
9
10
h > 1 or h ≤ -3
-4
-3
-2
-1
0
1
2
Homework
Practice worksheet 11.4 B
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1)
2)
3)
4)
5)
6)
7)
8)
x
x
x
x
≤
>
<
≥
50
70
2
3
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9)
10)
11)
12)
13)
Equation
x + 7 = 10
Left side
‘x’ has to be 3 in order
to make the equation
balanced.
Like a scale, the left
side and right side must
be the same in order to
be balanced!
Right side
How can you get the “unknown” by itself?
m + 24 = -18
“Undo” the operation by using the
INVERSE (opposite) operation to both
sides of the equation.
Solving Addition Equations…
Isolate the variable! Get ‘m’ by itself.
To get the ‘m’
by itself get rid of
“adding 24.”
m + 24 = -18
– 24 –24
Do the opposite.
“Subtract 24.”
Whatever you do to
one side of the equation
you must do the other side.
m = -42
-18 – 24
-18 + (-24) “opp-opp”
-42
Objective
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SWBAT solve one-step inequalities by
adding or subtracting
Section 11.5, “Solving Inequalities by
Adding or Subtracting”
INEQUALITIES –
mathematical sentence formed by
placing a <, ≤, >, or ≥ between two
expressions.
11 + a ≤ 121
Inequality
x + 7 > 10
Left side
‘x’ has to be greater
than 3 in order to make
the inequality a true
statement.
Right side
Writing Equations with
Inequalities
Symbol
Meaning
Key phrases
=
Is equal to
The same as
<
Is less than
Fewer than, below
≤
Is less than or equal At most, no more
to
than
>
Is greater than
More than, above
≥
Is greater than or
equal to
At least, no less
than
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On a number line, the GRAPH OF AN
INEQUALITY is the set of points that
represent the SOLUTION SET of the
inequality.
“Less than” and “greater
than” are represented
with an open circle.
Graph x < 8
5
6
“Less than or equal to”
and “greater than or equal
to” are represented with a
closed circle.
8
9
7
8
9
10
Graph x ≥ 11
10
11
12
13
14
11
Solving an Inequality…
Isolate the variable! Get ‘m’ by itself.
To get the ‘m’
by itself get rid of
“adding 4.”
m + 4 < 12
- 4 -4
Do the opposite.
“Subtract 4.”
Whatever you do to
one side of the Inequality
you must do the other side.
5
6
7
m<8
8
9
10
11
Solving an Inequality…
Isolate the variable! Get ‘n’ by itself.
To get the ‘n’
by itself get rid of
“subtracting 5.”
Do the opposite.
“Add 5.”
n-5≥ 6
+ 5 +5
Whatever you do to
one side of the inequality
you must do the other side.
8
9
10
11
n ≥ 11
12
13
14
Solve x – 5 > -3.5
Graph your solution
x – 5 > – 3.5
+5
+5
x > 1.5
Write original inequality.
Add 5 to each side.
Simplify.
ANSWER
The solutions are all real numbers greater
than 1.5. Check by substituting a number
greater than 1.5 for x in the original inequality.
Solve p – 9.2 < -5
Graph your solution
p – 9.2 < – 5
+ 9.2 + 9.2
p < 4.2
ANSWER
Write original inequality.
Add 9.2 to each side.
Simplify.
The solutions are all real numbers less than
4.2. Check by substituting a number less
than 4.2 for x in the original inequality.
Solve 9 ≥ x + 7
Graph your solution
9≥x+7
–7
–7
2≥x
Write original inequality.
Subtract 7 from each side.
Simplify.
ANSWER
You can rewrite 2 ≥ x as x ≥ 2.
The solutions are all real
numbers less than or equal
to 2.
Solve y + 5.5 > 6
Graph your solution
y + 5.5 > 6
–5.5 –5.5
y > 0.5
Write original inequality.
Subtract 5.5 from each side.
Simplify.
ANSWER
You can rewrite 0.5 < y as y > 0.5 . The
solutions are all real numbers greater than
or equal to 0.5 .
Solve a real-world problem
LUGGAGE WEIGHTS
You are checking a bag at an airport. Bags can weigh
no more than 50 pounds. Your bag weighs 16.8 pounds.
Find the possible weights w (in pounds) that you can
add to the bag.
SOLUTION
Write a verbal model. Then write
and solve an inequality.
16.8
+
w
≤
50
Solve a real-world problem
16.8 + w ≤ 50
– 16.8
–16.8
w ≤ 33.2
ANSWER
You can add no
more than 33.2 pounds.
Write inequality.
Subtract 16.8 from each side.
Simplify.
Homework
Text p. 490, #8-34 evens, 43 & 44