5(x+3)/6=4+3(x-1)/5 ANSWER: x = 27/7. Could someone please show me the steps as to how this final answer was derived? Thank you.
Now, we have to movie the terms that have variable x in them, to try to isolate it, so we subtract both sides by :
Next we find common denominator of these two fractions, which is 30:
Next we distribute and , and we multiply both sides by 30 to get rid of the denominator on the left side and we get 120 on the right side by multiplying 30 to 4.
Next we subtract 93 to both sides.
...and finally, divide by 7 to both sides.
I hope this is more clear.
Athough it is really the same thing, instead of getting a common denominator I would multiply through by 30:
(30)(5)(x+ 3)/6= 4(30)+ (30)(3)(x- 1)/5 and, since 30/6= 5 and 30/5= 6,
(5)(5)(x+ 3)= 4(30)+ 6(3)(x- 1)
25(x+ 3)= 120+ 18(x- 1).
Now we apply the "distributive law": a(b+ c)= ab+ ac. That is, 25(x+ 3)= 25x+ 25(3) and 18(x- 1)= 18x- 18(1). Of course, 25(3)= 75 so this becoes 25x+ 75= 120+ 18x- 18= (120- 18)+ 18x= 102+ 18x. Now, subtract 18 from both sides and subtract 75 from both sides to get
25x- 18x= 7x= 102- 75= 27. The last step is to divide both sides by 7: (7x)/7= x= 27/7.
here is how i would do it:
first i would get the 2nd side to "be one fraction", which means changing 4 to (1)(4) = (5/5)(4) = 20/5:
now we can add the numerators together, and we have:
since 3(x-1) = 3x - 3, 3(x-1) + 20 = 3x - 3 + 20 = 3x + 17 (i just took the 3 from the 20: the fewer terms, the better)
now, "cross-multiply": if a/b = c/d, then ad = bc. why does this work?
b(a/b) = b(c/d) (because a/b = c/d, so multplying them both by b still preserves the equality)
ab/b = bc/d...but ab/b = (a/1)(b/b) = (a/1)(1) = a/1 = a. so:
a = bc/d, and multplying both sides by d:
ad = (bc/d)d = (bc/d)(d/1) = (bc)(d/d) = (bc)(1) = bc, which is what i said was true up there a few lines ago.
so when we cross-multiply, we get:
look, no fractions! (i HATE fractions, every sane person should).
we can simplify the left side a bit, before we continue:
and we can also simplify the right side, as well:
(i used a calculator to calculate 6*17...so sue me)
so now we have:
this is looking better already.
subtracting 18x from both sides gives us:
subtracting 75 from both sides gives us:
and finally dividing both sides by 7 gives us:
it should comfort you that 3 different people using 3 different methods all give the same answer. we're all probably right. how do you make sure?
Thanks for all your help, guys! I will no doubt stumble across a similar question and once again ask for help. :S I've repped everyone in this thread for his useful help.