Download 12-4 Introduction to Inequalities WW: inequality, algebraic inequality

12-4 Introduction to Inequalities
WW: inequality, algebraic inequality, solution set,
EQ: Why can inequalities have more than one solution?
An inequality states that two quantities either are not equal
or may not be equal. An inequality uses one of the
following symbols.
Symbol
Meaning
<
is less than
>
is greater than
≤
≥
is less than or
equal to
is greater than
or equal to
Word Phrases
Fewer than, below, up
to
More than, above,
exceeds, in excess of
At most, no more than
At least, no less than
An inequality that contains a variable is an algebraic
inequality. A value of the variable that makes the inequality
true is a solution of the inequality.
An inequality may have more than one solution. Together,
all of the solutions are called the solution set.
Write each inequality in words
1)x > 7 a number greater than 7
2)h < -5 a number less than -5
3)d ≥ 23 a number greater than or equal to 23
4)r ≤ -2 a number less than or equal to -2
Write an inequality with the variable on the left.
1)19 < g
g > 19
3) 17 ≥ p
p ≤ 17
2)10 < e
e > 10
4) 0 ≤ f
f≥0
If x < 5, which of the following numbers are possible
solutions? -5, -8, 0, 5, 12, 18, -100, 234, 2
Solutions: {-5, -8, 0, -100, 2}
If x ≥ -10, which of the following numbers are possible
solutions? -7, 100, -10, 8, -15, -4, 9, -122, 0
Solutions: {-7, 100, -10, 8, -4, 9, 0}
Define a variable and write an inequality for each situation.
1)The highest temperature ever recorded on Earth was
135.9 degrees Fahrenheit at Al Aziziyah, Libya, on
September 13, 1922
t = temperature
t ≤ 135.9
2)The highest possible score on the SAT is 2400. Rebecca
scored 1780. She needs a score of at least 1950 to
qualify for a scholarship. How much higher must her
score, s, be?
a. s ≤ 170 b) s ≥ 170 c) s ≥ 450 d) s ≤ 450
The answer is b her score must be greater than or equal
to 170.
Graphing Inequalities
o Open dot = < or >
• Closed dot = ≥ or ≤
Shade right = ≥ or >
Shade left = ≤ or <
1) x > 9
<------------------------------------------------------->
2) x < 7
<------------------------------------------------------->
3) x ≤ 6.4
<------------------------------------------------------->
4) x ≥ 40
<------------------------------------------------------->
5) -2 < x
<------------------------------------------------------->
6) −1 ≥ x
<------------------------------------------------------->
Answer EQ: There are many numbers less or greater than a
single number.