Writing Inequalities
Solving Compound Inequalities with And
Solving Compound Inequalities with OR
Solving Absolute Value Inequalities
Solving Real Life Problems
100
A number x is greater than -8 and less than or equal to 4.
x>-8 and x<=4
100
-4<x-2<3
-2
100
3y-5<-8 or 2y-1>5
y<-1 or y>3
100
|2s-7|>=-1
All real numbers
100
A number p is less than 6 and greater than 2. Graph.
2
200
A number y is at most 0 or at least 2.
What is y<=0 or y>=2
200
-3<-2x+1<=9
-4<=x<2
200
v+8<3 or -8v<-40
v<-5 or v>5
200
3|14-m|>18
m>20 or m<8
200
A number m is more than -7.6 or at most -10. Graph
m>-7.6 or m<=-10
300
A number p is less than 6 and greater than 2.
2<p<6
300
6<x+5<=11
1<x<=6
300
2r+3<7 or -r+9<=2
r<2 or r>=7
300
2|3w+8|-13<=-5
-4<=w<= -4/3
300
The rules for an essay contest say that entries can have 500 words with an absolute deviation of at most 30 words. Write and solve an absolute value inequality that represents the acceptable number of words.
|w-500|<=30. 470 to 530 words
400
A number -7 2/3 or at most -10
m>-7 2/3 or m<=-10
400
-12<1/2(4x+16)<18
-10<x<5
400
2n+19<=10+n or -3n+3<-2n+33
all real numbers
400
If your C value is negative what are your two possible solutions?
Infinite or No Solution
400
An auto parts manufacturer throws out gaskets with weights that are not within 0.06 pound of the mean weight of the batch. The weights (in pounds) of the gaskets in a batch are 0.58, 0.63, 0.65, 0.53, and 0.61. Which gasket(s) should be thrown out?
The gasket with weight of 0.53lb
500
What's a compound inequality?
An inequality formed by joining two inequalities with the word "and" or the word "or."
500
22<-3c+4 and -3c+4<14
no solution
500
-3x+6<9 or -5x+10>15
x>-1 or x<-1
500
What is the solution of the inequality |ax+b|c, where c<0?
No solution. An absolute value cannot be negative. All real numbers. An absolute value must be positive or zero, so it will always be greater than any negative number.
500
Explain why the solution set of the inequality |x|<5 is the intersection of two sets, while the solution set of inequality |x|>5 is the union of two sets.
The solution of |x|<5 is the set of values that make both of 2 inequalities true, the solution |x|>5 is the set of values that make either of 2 inequalities true.
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