Inequalities

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Inequalities
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Inequalities

• An Equation is a mathematical relationship which
  is balanced - what is on the left is always equal
  to what is on the right
• In an Inequality, one side is larger than the
  other
• Womens average height is less than mens average
  height

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Inequlities

• To win a game of dice, a player must throw at
  least a score of 4 - i.e. equal to or greater
  than 4
• Score ³ 4
• There should be no more than 6 people standing on
  the bus - less than or equal to 6
• Number of people standing 6

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Inequality Signs

• lt means is less than
• ? means is less than or equal to
• gt means is greater than
• ? means is greater than or equal to

Reading Inequalities
6 lt 8 or equivalently 8 gt 6
n is greater than 3 but less than 9.
1. 3 lt n lt 9
n is greater than or equal to 4 but less than 7.
2. 4 ? n lt 7
n is greater than or equal to -2 but less than or
equal to 1.
3. -2 ? n ? 1
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Read the following inequalities
1. 0 lt n lt 3
n is greater than 0 but less than 3.
n is greater than or equal to -5 but less than 2.
2. -5 ? n lt 2
n is greater than or equal to -7 but less than or
equal to -1.
3. -7 ? n ? -1
x is greater than 9
4. x gt 9
x is greater than -1
5. x gt -1
p is greater than or equal to 6
6. p ? 6
a is greater than or equal to - 4
7. a ? - 4
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Displaying Inequalities on a Number Line
x ? 1
x ? -2
x gt 4
x gt 0
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Displaying Inequalities on a Number Line
x ? 1
x ? -2
x lt 4
x lt 0
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Displaying Inequalities on a Number Line
-5 ? n ? 5
-1 lt n ? 4
-5 lt n lt 0
-3 ? n lt 6
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State the inequalities displayed on each number
line below.
0 ? n ? 5
-5 lt n ? 4
0 lt n lt 5
-5 ? n lt -3
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Understanding Inequalities
In inequalities, the greater than sign (gt)
and the less than sign (lt) relate two expressions.
Divide both sides by -5 -2 lt - 3
FALSE
If both sides of an inequality are multiplied or
divided by a negative number, the inequality sign
is reversed to keep the inequality true.
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Graphing Linear Inequalities on a Number Line
Solve and graph x 8 gt 2 - 5x
x 5x gt 2 - 8 6x gt -6 x gt -1
The solid dot at -1 indicates that -1 is part of
the solution x gt 1 means x gt 1 and x 1
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Graphing Linear Inequalities on a Number Line
Solve and graph 2(x 3) - 5x lt x - 10
2x 6 - 5x lt x - 10 -3x 6 lt x - 10
-3x - x lt -10 - 6 -4x lt -16
x gt 4
Note the sign is reversed because both sides of
the inequality are divided by a negative number.
The open dot at 4 indicates that 4 is not part
of the solution.
2.1.4
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The rule for inequalities is
any time you multiply (or divide)
both sides by a negative number,
you need to reverse the signs.
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Solve each inequality
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Answers