SOLUTION: I have a problem with my homework. the answer in the book is not matching what I have come up with. I have even had my 9th grader work the problem and she comes up with the same an

Algebra ->  Inequalities -> SOLUTION: I have a problem with my homework. the answer in the book is not matching what I have come up with. I have even had my 9th grader work the problem and she comes up with the same an      Log On


   

Question 95746: I have a problem with my homework. the answer in the book is not matching what I have come up with. I have even had my 9th grader work the problem and she comes up with the same answer. I know that I have done the work right as this is the only problem I have trouble with and all of the other problems have the same answer. I will give you the problem and then show what I did. could you just check my work.
3/5x-2<3/10-x
3/5x-2<3/10-x
+x +x
+2 +2
3/5x+x<3/10+2
3/5x+x<23/10
then divided 3/5x by 3/5
and divided 23/10 by 3/5
flipped the 3/5 and multiplied the two fractions on the right like this...
x+x<23/10*5/3
2x<115/30
then divided the 2x by 2
and the 115/30 by 2
flipped the 2/1 to 1/2 and multiplied 1/2 with 115/30 like this...
x<115/30*1/2
x<115/60
which simplifies to...
x<23/12.
(-infinity,23/12)
The problem is the answer in the back of my book is (-infinity,23/16).
I have checked the problem in the book and the answer many times. Are my calculations correct?
Thank you...
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
%283%2F5%29x-2%3C3%2F10-x <==== OK
.
%283%2F5%29x-2%3C3%2F10-x
+x +x <==== adding x to both sides OK
+2 +2 <=== and adding 2 to both sides OK
%283%2F5%29x%2Bx%3C%283%2F10%29%2B2 <==== OK
%283%2F5%29x%2Bx%3C23%2F10+ <==== OK
.
then divided 3/5x by 3/5 <=== Nope. You forgot the +x on the left side. When you add
%283%2F5%29x+%2B+x+=+%283%2F5%29x+%2B+%285%2F5%29x you get %288%2F5%29x on the left side. At this point
the equation becomes: %288%2F5%29x+%3C23%2F10
.
and divided 23/10 by 3/5 <==== divide both sides by 8%2F5 to solve for x
.
flipped the 3/5 (should flip the 8/5) and multiplied the two fractions on the right like this...
.
x+x<23/10*5/3 <=== should be %285%2F8%29%2A%288%2F5%29x+%3C+%285%2F8%29%2A+%2823%2F10%29
.
2x<115/30 <=== disregard this. In the preceding step do the multiplication of both sides
by 5%2F8. The left side becomes just x because in the %285%2F8%29%2A%288%2F5%29 the
numerators
cancel the denominators. On the other side (the right side) the 5 in the numerator
reduces the 10 in the denominator to 2 ... so the multiplication becomes just:
.
%281%2A23%29%2F%288%2A2%29 and this simplifies to 23%2F16. So the inequality is reduced to:
.
x+%3C+23%2F16
.
the interpretation of this is that x can take any value less than 23%2F16 ... all the
way down to -infinity. So the answer is (-infinity,23/16)
.
Hope this helps you to understand the minor error you made. When you had %283%2F5%29x+%2B+x
you couldn't just divide the one term containing x by 3%2F5. You either had to add the
two terms containing x or you also had to divide the x by 3%2F5.