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

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) (Show Source): You can put this solution on YOUR website!
<==== OK
.

+x +x <==== adding x to both sides OK
+2 +2 <=== and adding 2 to both sides OK
<==== OK
<==== OK
.
then divided 3/5x by 3/5 <=== Nope. You forgot the +x on the left side. When you add
you get on the left side. At this point
the equation becomes:
.
and divided 23/10 by 3/5 <==== divide both sides by 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
.
2x<115/30 <=== disregard this. In the preceding step do the multiplication of both sides
by . The left side becomes just x because in the 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:
.
and this simplifies to . So the inequality is reduced to:
.

.
the interpretation of this is that x can take any value less than ... 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
you couldn't just divide the one term containing x by . You either had to add the
two terms containing x or you also had to divide the x by .
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