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Solving/Graphing Inequalities

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.

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.

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.

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.

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

{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