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Question 150374: 1. Marika is a salesperson who must decide between two monthly income options:
Option 1: Salary of $1412 per month, plus 10% of monthly sales
or Option 1: Salary of $2000 per month, plus 6% of monthly sales
What must the monthly sales amount be so that Option 1 is a better choice for Marika than Option 2?
Show a correct inequality and solve it.
2. Solve (x + 5)(x – 4)(x – 7) <= 0 and write the solution set in interval notation. Show all work
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1. Marika is a salesperson who must decide between two monthly income options:
Option 1: Salary of $1412 per month, plus 10% of monthly sales
s1(x) = 1412 + 0.10x
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Option 1: Salary of $2000 per month, plus 6% of monthly sales
s2(x) = 2000 + 0.06x
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What must the monthly sales amount be so that Option 1 is a better choice for Marika than Option 2?
INEQUALITY:
s1 < s2
1412 + 0.10x < 2000 + 0.06x
0.04x = 588
x = $14700
Show a correct inequality and solve it.
Done
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2. Solve (x + 5)(x – 4)(x – 7) <= 0 and write the solution set in interval notation. Show all work
1st Solve the Equality:
x = -5 or 4 or 7
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2nd: Draw a number line and mark those x-values on the line.
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3rd: Solve the Inequality (x + 5)(x – 4)(x – 7) < 0
try a test point in each interval to see where the solution set is:
try x = -6; -1*-10*-13 <0; true so solutions in (-inf,-5)
try x = 0 ; 5*-4*-7 < 0 ; false so no solutions in (-5,4)
try x = 5 ; 10*1*-2 < 0 ; true so solutions in (4,7)
try x = 8 ; 13*4*1 < 0 ; false so no solutions in (7,+inf)
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Final Answer: (-inf,-5) U (4,7)
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Cheers,
Stan H.
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