Surprise!
How is an inequality different than an equation?
- symbols
- equations just have ONE solution, where inequalities have more than one
4x + 5 = 17
x = 3
2x + 11 > 23
x > 6
Sara charges a fee of $30 and $5 an hour to tutor people in math. If she made $80, how many hours did she work?
Write an equation for this situation.
5x + 30 = 80 or 30 + 5x = 80
5x + 10 = 40
Check if x = 4 is a solution to the inequality above by substituting it in.
5(4) + 10 = 40
20 + 10 = 40
30 = 40
FALSE, so no.
x/7 + 3 = 8
x=35
5x - 9 < 11
x < 4
A cable company charges $50 per visit and $20 for each device they install. If you owe $130 how many devices did you get?
Write an equation for this situation.
50 + 20x = 130 or
20x + 50 = 130
How do you know when you flip the sign when solving an inequality? Give an example
When you divide or multiply by a negative
2(3x+6)=30
x = 3
-3x + 9 > 36
x < -9
Sarah earns $20 an hour and already has $100 saved. When will she have more than $300?
Write an inequality for this situation.
20x + 100 > 300
2x - 8 < 11
Check if x = 3 is a solution to the inequality above by substituting it in.
2(3) - 8 < 11
6 - 8 < 11
-2 < 11
TRUE So yes!!
-4( 2x + 4) = -56
x = 5
SOLVE AND GRAPH
x/2 + 6 >= 13
x>= 14
A teacher can have no more than 30 students in the class. If they already have 9, how many more students can join?
Write an inequality for this situation.
x + 9 <= 30
Find the error.
-4(2x - 3) - x = 6
-8x - 12 - x = 6
-9x - 12 = 6
+12 +12
-9x = 18
x = -2
Negative times a negative is a positive!!!
-3(x-2)+5x=10
x=2
Solve AND GRAPH
-5x - 12 > 23
x < -7
Tickets to a show cost $7 each and parking is $8. A group of friends can spend no more than $50. How many tickets can they buy?
Write an inequality to represent this situation.
7x + 8 <= 50