Show:
Solving Simple Inequalities
Multi Step Inequalities
Compound Inequalities
Absolute Value Inequalities
Graphing Inequalities
100
What is the first step in solving this problem: -5x >20
Divide both sides by -5
100
In the multi step inequality below what should be the FIRST thing you do: 5( x+ 4) -8 < 8 + 9 (x-3)
DISTRIBUTE the 5 on the left side and the 9 on the right side
100
What are the two types of compound inequalities that we talked about and describe them
and - intersections- both inequalities have to be true or- unions- at least one inequality has to be true
100
What is absolute value and what is special about it
It is the distance from 0 It must always be positive!
100
What is the difference between less than and less than or equal to on a number line graph
less than uses an open circle less than or equal to uses a closed circle
200
If you add a negative number to both sides what happens to the sign of the inequaltiy
Nothing! The sign only changes direction when you multiply or divide by a negative number on both sides!
200
How can you make your life easier when solving this inequality: 1/3 (x + 8) - 7 > 2/6 + 2/3(X-5)
Change the 1/3 to 2/6 and the 2/3 to 4/6 Then get rid of the fractions by multiplying both sides by 6
200
Is this an "and" or an "or" inequality? -6 < 3x + 2 < 8
AND
200
When you have a problem that uses > sign with an absolute value which compound inequality do you use?
OR
200
What is the difference between greater than and greater than or equal to on a coordinate plane graph
greater than uses a dashed line greater than or equal to uses a solid line
300
x + 9 < -43
x < -52
300
I have $15 to spend at the store. I buy $ 8 worth of chips. I want to spend the rest of my money on candy. How many pieces of candy can I buy if each reeses cup costs $0.35?
.35 x + 8 < 15 .35 x < 7 x < 20 I can buy no more than 20
300
Solve and Graph: 5x + 8< 28 and -5 < 10x
x< 4 AND x> -1/2
300
When do you utilize the AND
when its <
300
When do you HAVE to use a coordinate plane graph for an inequality?
When your inequality has two variables
400
-3/4x > 12
-3x >48 x< -16
400
Solve: 1/3 (x + 5) -4 < -9( x-2) -7x
2/3x + 5/3 -5 < -9x +18 -7x 2x +5 -15 < -27x + 54-21x 2x - 10< -48x -54 50x - 10 < -54 50x < -44 x< -44/50 x< -22/25
400
SOLVE and GRAPH: 3x +2 < 11 or 5x -8> 22
x < 3 OR x> 6
400
SOLVE and graph: I 2c + 3 I < 11
2c +3 < 11 AND 2c + 3> -11 2c <8 AND 2c>-14 c<4 AND 2c >-7
400
Graph: Y > 3x + 7
Y intercept (0,7) SLOPE 3/1
500
2/3 x + 8 > 1/3 x + 9
1/3 x > 1 x> 3
500
The drama club collected $160 from ticket sales for the spring play. They need to collect at least $400 to pay for new lighting. If the tickets sold for $3 each, how many more tickets need to be sold to earn at least $400?
160 + 3x > 400 3x> 240 x> 80 They need to sell 80 or more tickets
500
What other inequality type utilizes compound inequalities and why?
Absolute Value because absolute value always has two options for answers because the absolute value of a positive or a negative number is the same
500
SOLVE and GRAPH: I (4b-2)/3 I > 12
(4b-2)/ 3 > 12 OR (4b-2)/3 < -12 4b-2 > 36 4b - 2 < -36 4b > 38 4b < -38 b> 9.5 b< -9.5
500
GRAPH: 8x - 12y < 36
-12y < -8x + 36 y > 8/12 x - 3 Y int (0, -3) slope: 8/12