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# Solve the linear inequality.

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1019
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It is estimated that the annual cost of driving a certain new car is given by the formula

C = 0.39m + 2600

where m represents the number of miles driven per year and C is the cost in dollars. Jane has purchased such a car and decides to budget between \$6890 and \$8840 for next year's driving costs. What is the corresponding range of miles that she can drive her new car?

Jun 26, 2014

#4
+33568
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I don't like inequalities!  I try to turn them into equalities.  We can do this here by separately finding the two extremes:

1. 0.39m1 + 2600 = 6890

Subtract 2600 from both sides:  0.39m1 = 4290

Divide both sides by 0.39:  m1 = 4290/0.39 = 11000

2. 0.39m2 + 2600 = 8840

Subtract 2600:  0.39m2 = 6240

Divide by 0.39: m2 = 6240/0.39 = 16000

Hence the range is between 11000 and 16000 miles.

Jun 26, 2014

#1
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try solving the following based on the techniques that I posted in response to one of your earlier questions!  If you get stuck or want to verify your work feel free to post and we can discuss

6890<C<8840

6890<39m+2600<8840

Jun 26, 2014
#2
+253
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I did

6890<39m+2600<8840    subtract 39 on 3 sides and get 6890m<+2600<8801

then i divide by 39 and get 17.6<+13.9<22.9

Jun 26, 2014
#3
+576
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In this case we cannot subtract 39. In algebra we always need to look for inverses (opposites) to cancel things out.  When we look at the original setup the 39 is connected to the m by multiplication and then 2600 is added.  We have two options: a, cancel out the multiplication with division or b, cancel out addition with subtraction.  We should pause for a moment to see which one is easier.  If we choose division we need to divide by 39, which is possible but not fun particulalry in the middle piece because we end up with "m+2600/39" and now we have all sorts of fractions to deal with.  Its much easier to subtract 2600

6890<39m+2600<8840

4290<39m<6240

From here your idea to divide by 39 is spot on.  Our result is

110<m<160

Jun 26, 2014
#4
+33568
+5

I don't like inequalities!  I try to turn them into equalities.  We can do this here by separately finding the two extremes:

1. 0.39m1 + 2600 = 6890

Subtract 2600 from both sides:  0.39m1 = 4290

Divide both sides by 0.39:  m1 = 4290/0.39 = 11000

2. 0.39m2 + 2600 = 8840

Subtract 2600:  0.39m2 = 6240

Divide by 0.39: m2 = 6240/0.39 = 16000

Hence the range is between 11000 and 16000 miles.

Alan Jun 26, 2014
#5
+576
0

Glad I saw your post, Alan.  In my inital setup i missed a decimal point accompanied with 39 so my answers were off by a factor of 100!

Jun 26, 2014
#6
+33568
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Never mind; what's a factor of 100 among friends!

Jun 26, 2014