SOLUTION: 1. 3/4x-(x-5)/3=x/2 2. t-12/5+3t/4=(t-6)/2 solve for X 3. x+a/3=c 4. ax+b=cx 5. 3ax-b=d-4cx

Algebra ->  Equations -> SOLUTION: 1. 3/4x-(x-5)/3=x/2 2. t-12/5+3t/4=(t-6)/2 solve for X 3. x+a/3=c 4. ax+b=cx 5. 3ax-b=d-4cx      Log On


   

Question 112988: 1. 3/4x-(x-5)/3=x/2
2. t-12/5+3t/4=(t-6)/2
solve for X
3. x+a/3=c
4. ax+b=cx
5. 3ax-b=d-4cx
Answer by veronica0626(5) About Me  (Show Source):
You can put this solution on YOUR website!
1. 3%2F4x-%28x-5%29%2F3=x%2F2
first get the LCD of 3 and 4x, which is 12x.
divide 12x by the denominator 4x you get a 3.
multiply to the numerator 3.
do the same thing with the second term.
%283%2A3%29-%284%2Ax%29%28x-5%29%2F%283%2A4x%29=x%2F2
multiply and you will get
%289-4%2Ax%5E2%2B20%2Ax%29%2F12%2Ax%5D=x%2F2
cross multiply
(equate the product of 12x and x
with the product of (9-4x^2+20x) and 2)
12x%2Ax=%289-4x%5E2%2B20x%29%2A2
12x%5E2=18-8x%5E2%2B40x
transpose everything to the left side and you get
20x%5E2-40x-18=0
divide the left side by 2 and you get
10x%5E2-20x-9=0
use the formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
by substituting a=10, b=20, and c =9
x=%28-20%2B-sqrt%2820%5E2-4%2A10%2A9%29%29%2F2%2A10
x=%28-20%2B-sqrt%28400-360%29%29%2F20
x=%28-20%2B-sqrt%2840%29%29%2F20
x=%28-20%2B-2%2Asqrt%2810%29%29%2F20
finding the lowest term we have
x=%28-10%2B-sqrt%2810%29%29%2F10

2. %28t-12%29%2F5%2B3t%2F4=%28t-6%29%2F2
get the LCD and find the new numerator
%284%2A%28t-12%29%2B5%2A%283t%29%29%2F20=%28t-6%29%2F2
multiply and simplify
%284t-48%2B15t%29%2F20=%28t-6%29%2F2
19t-48%29%2F20=%28t-6%29%2F2
cross multiply
38t-96=20t-120
divide both side by two and we get
19t-48=10t-60
combine like terms and we get
9t=-20
then we have t=%28-20%29%2F9

solve for X
(in terms of a nd c)
3. %28x%2Ba%29%2F3=c
cross multiply and equate
x%2Ba=3c
subtract a to both side of the equation and u get
x=3c-a
4. ax%2Bb=cx
subtract b+cx on both side and we get
ax-cx=-b
rewrite ax-cx
x%2A%28a-c%29=-b
divide (a-c) on both side and we get
x=%28-b%2F%28a-c%29%29
5. 3ax-b=d-4cx
add 4cx%2Bb on both side and we get
3ax%2B4cx=d%2Bb
rewrite (3ax+4cx)
x%283a%2B4c%29=d%2Bb
divide both side by (3a+4c)
x=%28%28d%2Bb%29%2F%283a%2B4c%29%29