solving an equation for a variable?

Question

x/a + y/b + z/c = 1

how do you solve for a?

i know its prob pretty easy and the answer's right in front of me, but i keep going in loops...

Answer 1

You have to isolate a on one side of the equation.

Step one: subtract y/b and z/c from both sides

x/a = 1 - y/b - z/c

Step two: take the reciprocal of both sides

a/x = 1 / (1 - y/b - z/c)

Step three: multiply both sides by x

a = x / (1 - y/b - z/c)

Answer 2

The easiest way is to multiply both sides by every value found in the denominators. In this case, multiply both sides by abc:

x/a + y/b + z/c = 1
( x/a + y/b + z/c) * abc = 1 * abc
( x/a ) * abc + ( y/b ) * abc + ( z/c ) * abc = abc
xbc + yac + zab = abc

Now you need to put every a on one side of the equation:
    xbc = abc - yac - zab
Factor out an a on the right side:
    xbc = a ( bc - yc - zb )
Then divide both sides by ( bc - yc - zb ):
    a = xbc / ( bc - yc - zb )

Answer 3

you would subtract y/b and z/c from 1. then you would multply both sides times a. at this point youre left with only x on the left side of the equation. at which point you will divide everything besides a on both sides. leaving you with x/(1-y/b -z/c)=a.

Answer 4

a = (1 - (y/b) - (z/c))/ x

Answer 5

Multiply both sides by a:

a(x/a + y/b + z/c) = a

Distribute:

x + ay/b + az/c = a

Subtract ay/b + az/c from both sides:

x = a - ay/b - az/c

Collect your terms:

x = a(1 - y/b - z/c)

Divide by (1 - y/b - z/c):

a = x/(1 - y/b - z/c)

And there's your answer.

Answer 6

ok, do it one step-at-time and you will locate that t = + one million: (one million) Algebraically upload "like" words: 9 - 6 = 3 and -t - t = -2t (2) So, on the left-area, you have: 3 - 2t and on the properly suited you nonetheless have t (3) Now, upload 2t to the two aspects and you presently have: 3 = 3t, on account that -2t + 2t = 0 (on the left area) at the same time as t + 2t = 3t (on the properly suited area) (4) finally, divide the two aspects by utilising 3 and you presently have one million = t or (what's an identical situation) t = one million. notice: in case you are able to shelter trouble-free math, you're able to no longer get right into a tangle. and don't be intimidated by utilising "variables"; in trouble-free algebra, geometry, trig, and so on. they are in basic terms symbols that in many circumstances designate numbers!!! additionally, you're able to desire to get used to the "shorthand", at the same time with (in the above): 2t potential "2 expanded by utilising t", and -2t potential "minus one million expanded by utilising 2 expanded by utilising t", and the expression -2t + 2t = 0 potential that "that sum is often 0, no count the value of t", and so on. have fun with!!!!

Answer 7

(x/a) + (y/b) + (z/c) = 1
Multiply everything by abc
xbc + yac + zab = abc
subtract xbc and abc from both sides
yac + zab - abc = -xbc
factor the left side
a(yc + zb - bc) = -xbc
divide both sides by (yc + zb - bc)
a = (-xbc)/(yc + zb - bc)

Answer 8

x/a+ y/b+z/c=1
x/a=1-(y/b)-(z/c)
1/a=(1-(y/b)-(z/c))(x)
a=1/(x-(xy/b)-(xz/c))