Solving Equations
Is x = 9 a solution to the equation
3x - 8 = 16
NO
What makes an equation literal?
An equation that has multiple variables
What are the four types of inequalities?
- Less than <
- Greater Than >
- Less than or equal to ≤
- Greater than or equal to ≥
What are the three parts of an inequality that we need to graph?
-Max/Min (Boundary Point)
-Less than or greater than
-Equal to?
Sally has 28 Jelly beans and wants to share them evenly between her and her 3 best friends. How many jelly beans will each of them get?
7 Jelly Beans
2x - 4 = 8
x = 6
Solve for x:
2x - b = a
(a+b)/2
Solve for x:
2x + 4 < -6
x < -5
Write the inequality that matches the graph:
o------------------------------>
___________________________
-10 -5 0 5 10
x > -10
Multiple Choice:
Andy makes $8.25 an hour, plus tips. If his goal is to make at least $750 this summer and makes $330 in tips, which inequality best represents this situation.
A) 8.25h + 750 = 330 B) 750 + 330 ≥ 8.25h
C) 75 - 330h = 8.25 D)8.25h + 330 ≥ 750
D) 8.25h + 330 ≥ 750
Solve for x
4x + 7 = 1/2(6x - 10)
x = -12
Solve for b:
A = (1/2)bh
b = 2A/h
3 ( 4/3 x - 4) ≥ 16
x ≥ 7
Graph the Inequality:
4 < x
o---------->
________________________
-10 -5 0 5 10
Write an inequality that matches the statement:
Professor Plum has a total of 200 students in his classes. He knows that 80 of his students don't prefer music over sports. If there is an average of 24 students in each class that prefer music over sports, how many classes does Professor Plum have?
80 + 24x = 200
Solve for x:
2(2x+4) = 6 + 4x + 2
Infinite Solutions
Solve for y:
2x+3y = 12
y = 4 - 2/3x
-3x + 4 - 1 > 9
x < -2
Solve and graph the inequality:
2x - 3 ≥ 7
x ≥ 5
● ----------->
_____________________________
-10 -5 0 5 10
Bradley wants to at least $250 left over at the end of the summer. He starts with 500, but spends $30 per comic book. However, for every comic book he buys he makes $3 back. How many comic books can he buy to have enough money left over at the end of summer.
9 comic books
Solve for x
3/8(x-16) = 6
x = 32
Solve for x:
y = 3(2x+6)-12
x = 1/6y - 1
Samantha has $550 that she is allowed to spend. She wants to buy a $200 tv and as many $45 games that she can.
Write an inequality that represents this situation and determine the MAX number of games she can buy.
550 ≥ 200 + 45x
x = 8 Games
Write and graph the inequality that matches the situation:
Terrance must be older than 13 to ride the Mr Freeze.
x > 13
o------->
_________________________________
-15 -10 -5 0 5 10 15
Nacho Libre has $60 to spend at the fair. He spends $15 to get in and wants to buy as many $13 raffle tickets as possible. Write an inequality that matches this statement and determine how many raffle tickets he can buy.
15 + 13r ≥ 60
4 Raffle Tickets