Compound Inequality, Selling Price Range, and Retirement pay
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Solve each compound inequality and write the solution set using interval notation.
80)
0< 5-2x <=10
-6< 4-x<0
81)
-3 < (3x -1)/ 5 < ½
1/3 < (3-2x)/6 < 9/2
86) Selling Price Range: Renee wants to sell her car through a broker who charges a commission of 10% of the selling price. The book value of the car is $14,900 but Renee still owes $13,104 on it. Although the car is in fair condition, and will not sell for more than the book value Renee must get enough to at least pay off the loan. What is the range of selling price?
54 ) Retirement pay: The annual Social Security benefit of a retiree depends on the age at the time of retirement. The accompanying graph gives the annual benefit for persons retiring at ages 62 through 70 in the year 2005 or later.
What is the annual benefit for a person who retires at the age of 64?
At what retirement age does a person receive an annual benefit of $11,600?
Find the slope of each line segment on the graph and interpret your results.
Why do people who postpone retirement until 70years of age get the highest benefit?
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The solution solves questions on compound inequality, selling price range, retirement pay.
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80) 0< 5-2x <=10
-6< 4-x<0
Solving the first inequality:
0< 5-2x <=10
5-2x>0
or 5>2x
or x< 2.5
5-2x <=10
or 5-10 <=2 x
or x >= - 2.5
Solving the second inequality:
-6<4-x <0
4-x< 0
or x>4
4-x>-6
or x<10
Thus
From the first inequality
-2.5<=x< 2.5
Thus x lies in the region from -2.5 to 2.5
and from the second inequality
4<x<10
Thus x lies in the region from 4 to 10
Since these two regions do not overlap there is no solution.
81)
-3 < (3x -1)/ 5 < ½
1/3 < (3-2x)/6 < 9/2
Solving the first inequality:
-3 < (3x -1)/ 5 < ½
(3x -1)/ 5 < ½
or 3x -1 < 5/2
or 3x < 7/2
or x < 7/6
-3 < (3x -1)/ 5
or 3x-1 > ...
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