Solving/Graphing Inequalities
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This solution includes several problems on solving and graphing inequalities. Detailed solutions are provided to explain the concept.
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This solution includes several problems on solving and graphing inequalities. Detailed solutions are provided to explain the concept.
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Week 8
1.) Determine whether the given numbers are solutions of the inequality.
4,-19,-10,-1
y-8>2y-3
Is 4 a solution? __________no ___________yes
Solution:
y-8>2y-3
4 - 8 > 2*4 - 3
-4 > 5
So 4 is not the solution.
Answer: NO
Is -19 a solution? __________no __________yes
Solution:
-19 -8>2y-3
-27 > 2*(-19) - 3
-27 > - 41
It is possible so -19 is solution of the given inequality.
Answer: YES
Is -10 a solution? __________no __________yes
Solution:
-10 -8>2y-3
-18 > 2*(-10) - 3
-18 > - 23
It is possible so -10 is solution of the given inequality.
Answer: YES
Is -1 a solution? ___________no _________yes
Solution:
-1 -8>2y-3
-9 > 2*(-1) - 3
- 9 > - 5
It is not possible so -1 is not the solution of the given inequality.
Answer: NO
1.) Write the set {x |x in interval notation.
(-infinity, -1]
2.) Write interval notation for the set {x|-5>x>-10}.
Choose the correct interval notation below.
a.) (-10,-5]
b.) [-10,-5]
c.) (-10,-5)
d.) [-10,-5)
Answer: (-10, -5) (because -10 and -5 are not included)
5.) Solve. Then graph.
t+16 5
The solution is {t|t __}
Solution:
t+16 5
Subtract 16 from each side, we will get
t+16 - 16 5 - 16
t - 11
Answer:
{t|t -11}
6.) - x
The solution set is {x|x ___ _____}
( Simplify your answer. Type an equality symbol: then type an integer or a fraction)
Solution:
Multiply each side by - 2/9, we will get
Answer:
The solution set is {x| }
7.) Solve
9x+7<43
The solution is {x|x ___ _____}
( Simplify your answer. Type an equality ...
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