Unit 8 Solving Inequalities Vocabulary Inequality A mathematical sentence that compares two unequal expressions using one of the symbols lt less than gt greater than less than or equal to ID: 598153
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Slide1
Equations and InequalitiesSlide2
Unit 8 – Solving InequalitiesSlide3
Vocabulary
Inequality
– A mathematical sentence that compares two unequal expressions using one of the symbols:
< (less than)
> (greater than)
≤ (less than or equal to)
≥ (greater than or equal to)
≠ (not equal to)
Closed Circle
-
Includes a quantity on a number line.
Used with ≤ or ≥.
Open Circle
-
Does not include a
quantity on a number line.
Used with < or >.Slide4
Solving Simple Inequalities - Example
>
=
Complete with =, < or >.
>
<Slide5
Determining Solutions for Inequalities Example
Determine 4 solutions for each inequality. Then represent the solutions of each inequality on a number line.
y
> 7
When
y
= _____,
y
> 7 is true.
When
y = _____, y > 7 is true.When y = _____,
y > 7 is true.
When
y = _____,
y
> 7 is true
.
The inequality y > 7 is true for any value of y that is greater than 7.Slide6
Determining Solutions for Inequalities Example
Determine 4 solutions for each inequality. Then represent the solutions of each inequality on a number line.
m
< 28
When
m
= _____,
m
< 28 is true.
When
m = _____, m < 28 is true.When m =
_____,
m < 28 is true.
When
m
=
_____,
m < 28 is true.The inequality m < 28 is true for any value of m that is less than 28.Slide7
Determining Solutions for Inequalities Example
Determine 4 solutions for each inequality. Then represent the solutions of each inequality on a number line.
e
≥
15
When
e
= _____,
e
≥ 15 is true.When e = _____,
e
≥ 15 is true.
When
e
=
_____,
e ≥ 15 is true.When e = _____, e
≥
15
is true
.
The
inequality
e
≥ 15 is true for any value of e that is greater than or equal to 15.Slide8
Determining Solutions for Inequalities Example
Determine 4 solutions for each inequality. Then represent the solutions of each inequality on a number line.
z
≤
21
When
z
= _____,
z ≤ 21 is true.When z
= _____, z
≤ 21 is true.
When
z
=
_____, z ≤ 21 is true.When z = _____,
z
≤
21
is true
.
The
inequality z ≤ 21 is true for any value of z that is less than or equal to 21.Slide9
Determining Solutions for Inequalities Practice
Determine 4 solutions for each inequality. Then represent the solutions of each inequality on a number line.
p
< 45
p
could equal any number less than 45
a
> -57
a could equal any number greater than -57 n ≤ 17n could equal any number less than or equal to 17
w
≥ -63
w
could equal any number
greater than or equal to -63
Slide10
Writing Inequalities from Number Lines - Example
Write an inequality for each number line using the variable
a
.
a
> 14Slide11
Writing Inequalities from Number Lines - Example
Write an inequality for each number line using the variable
a
.
a
≤
15Slide12
Writing Inequalities from Number Lines - Practice
Write an inequality for each number line using the variable
a
.
a
≥
11
a
< 14