Download Notes: Solving Inequalities Using Addition and Subtraction

Notes: Introduction to Inequalities
Reminders:
<: ___________________________ ≤: _______________________________________
>: ___________________________ ≥: _______________________________________
Solution of an Inequality: any number that makes the inequality __________.
(ex) x > 4: all real numbers greater than 4
(ex) x ≤ –3: all real numbers less than or equal to –3
Example 1: Determine if each number is a solution of the given inequality.
*Substitute the given number in for x. After you simplify everything, decide if it’s a true statement. If it is,
the answer is yes. If it’s a false statement, the answer is no.
(a)
3 + 2x < 8
–2:
(b)
3:
6x – 3 > 10
2:
3:
The solution of an inequality isn’t just one number! We can use a graph to show all solutions.
Graphing Inequalities
Circles
Shading
__________: > or <
__________: less than (< or ≤)
__________: ≥ or ≤
__________: greater than (> or ≥)
Example 2: Graph.
*Trick: If the variable is on the LEFT side of the inequality symbol, you can turn the inequality symbol into
an arrow and the arrow will point in the direction you are supposed to shade!
(a)
x<3
(b)
x ≥ –2
(c)
4≥x
Common Inequality Translations
<: less than
>: greater than, more than
≤: less than or equal to, at most, no more than, no greater than, at or below, maximum, up to
≥: greater than or equal to, at least, no less than, minimum
Example 3: Define a variable and write an inequality for each situation.
*Define a variable based on what the statement is talking about. Write that variable on the left. Write
the number that is used in the problem on the right. In the middle, write the inequality symbol.
(a)
A speed that violates the law when the speed limit is 55 mph.
(b)
A job that pays at least $500 a month.
(c)
A class can hold at most 30 students.
(d)
The concert must sell more than 80 tickets to make a profit.