Make x the subject?

Question

1. 4(x-2y)=3(2x-y) (Make x the subject)
2. p(a-b)=q(a+b) (Make a the subject)
3. A=2ab^2 + ac (Make a the subject)
4. s(t+1)=2r+3 (Make r the subject)
5. st-r=2r-3t (Make t the subect)
6. ax=b-cx (Make x the subject)
7. x(a-b)=x+b (Make x the subject)
8. a-bx=dx-a (Make x the subject)
9. x(c-d)=c(d-x) (Make x the subject)
10. P=2 pi r + 4r (Make r the subject)
11. A= pi r ^2 + 4r^2 (Make r the subject)
12. y=x+2/x+3 (Make x the subject)
13. y=2-3x/x-1 (Make x the subject)
14. a=2+3a/b-2 (Make a the subject)

Help would be greatly appreciated.

Answer 1

Hi,



To solve for another variable:

a) Eliminate any fractions and/or parentheses.

b) Move all the terms with the subject variable to one side of the equation and move all terms without the subject variable to the other side of the equation. Combine any like terms.

c) Factor the subject variable out as a GCF on one side of the equation.

d) Divide both sides of the equation by the expression left behind when taking out the GCF. This gets the subject variable alone.

e) If the subject variable is squared, take the square root of both sides. Remember this could require a +/- sign in front of the remaining radical. In this case on # 11, since "r" is the radius and it is always positive, the +/- sign is not needed.



1. 4(x-2y)=3(2x-y) (Make x the subject)

4x - 8y = 6x - 3y

-2x = 5y

x = -5/2y <== ANSWER



2. p(a-b)=q(a+b) (Make a the subject)

pa - pb = qa + qb

pa - qa = pb + qb

a(p - q) = pb + qb

a = (pb + qb)/(p - q) <== ANSWER



3. A=2ab^2 + ac (Make a the subject)

A = a(2b² + c)

a = A/(2b² + c) <= ANSWER



4. s(t+1)=2r+3 (Make r the subject)

st + s = 2r + 3

st + s - 3 = 2r

r = (st +s - 3)/2 <== ANSWER



5. st-r=2r-3t (Make t the subect)

st + 3t = 3r

t(s + 3) = 3r

t = (3r)/(s + 3) <== ANSWER



6. ax=b-cx (Make x the subject)

ax + cx = b

x(a + c) = b

x = b/(a + c) <== ANSWER



7. x(a-b)=x+b (Make x the subject)

ax - bx = x + b

ax - bx - x = b

x(a - b - 1) = b

x = b/(a - b - 1) <== ANSWER



8. a-bx=dx-a (Make x the subject)

-dx - bx = -2a

dx + bx = 2a

x(d + b) = 2a

x = (2a)/(d + b) <== ANSWER



9. x(c-d)=c(d-x) (Make x the subject)

cx - dx = cd - cx

2cx - dx = cd

x(2c - d) = cd

x = (cd)/(2c - d) <== ANSWER



10. P=2 pi r + 4r (Make r the subject)

P = r(2 pi + 4)

r = P/(2 pi + 4) <= ANSWER



11. A= pi r ^2 + 4r^2 (Make r the subject)

A = r²( pi + 4)

A/( pi + 4) = r²

r = sqrt( A/( pi + 4)) <== ANSWER



12. y=x+2/x+3 (Make x the subject)

I assume this is y = (x + 2)/(x + 3).



y(x + 3) = x + 2

xy + 3x = x + 2

xy + 2x = 2

x(y + 2) = 2

x = 2/(y + 2) <== ANSWER



13. y=2-3x/x-1 (Make x the subject)

I assume this is y = (2 - 3x)/(x - 1).



y(x - 1) = 2 - 3x

xy - y = 2 - 3x

xy + 3x = 2 + y

x(y + 3) = 2 + y

x = (2 + y)/(y + 3) <== ANSWER



14. a=2+3a/b-2 (Make a the subject)

I assume this is a = (2 + 3a)/(b - 2).



a(b - 2) = 2 + 3a

ab - 2a = 2 + 3a

ab - 5a = 2

a(b - 5) = 2

a = 2/(b - 5) <== ANSWER



I hope those help!! :-)

Answer 2

The object is to get x on its own. First, you should multiply out the brackets.



e.g. (1)



4(x-2y) = 3(2x-y)

4x-8y = 6x-3y



Then you should get all of the x's on one side, and the y's on the other, by adding and subtracting



4x - 8y = 6x - 3y

- 5y = 2x



Then you need to get rid of the coefficient of x by dividing by 2



x = (-5y)/2

Answer 3

howdy Your answer is nice. do no longer ignore that with an equation in case you do a similar difficulty to each aspect, it truly is going to nonetheless be equivalent. Now hence the difficulty we do to each aspect is subtract 3y from each aspect. this provides x + 3y - 3y = 5v - 3y. now the +3y - 3y on the left cancel so that you ultimately end up with x = 5v - 3y ok? John B

Answer 4

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Answer 5

Hi Dear;Did you mean:

1.

4x-8y=6x-3y

2x= -5y

x=(-5\2)y

.......................................

2.

pa-pb=qa+qb

pa-qa=pb+qb

(p-q)a=(p+q)b

a=(p+q)b\(p-q)

.......................................

3.

2ab^2+ac-a=0

a(2b^2+c-1)=0

a=0

or:

a(2b^2+c)=A

a=A\(2b^2+c)

.......................................

4.

2r=s(t+1)-3

r=[s(t+1)-3]\2

.......................................

5.

st+3t=3r

(s+3)t=3r

t=(3r)\(s+3)

.......................................

6.

ax+cx=b

(a+c)x=b

x=b\(a+c)

.......................................

7.

(a-b)x-x=b

(a-b-1)x=b

x=b\(a-b-1)

.......................................

8.bx+dx=2a

(b+d)x=2a

x=(2a)\(b+d)

.......................................

9.

(c-d)x=cd-cx

(2c-d)x=cd

x=(cd)\(2c-d)

.......................................

10.

P=r(2pi+4)

r=P\(2pi+4)

.......................................

11.

A=pi r^2+4r^2

(pi+4)r^2=A

r^2=A\(pi+4)

r=[A\(pi+4)}^(1\2)

.......................................

12.

x+2=xy+3y

xy-x=2-3y

(y-1)x=2-3y

x=(2-3y)\(y-1)

.......................................

13.

2-3x=xy-3y

xy+3x=3y+2

(y+3)x=3y+2

x=(3y+2)\(y+3)

.......................................

14.

2+3a=(b-2)a

(b-2)a-3a=2

(b-5)a=2

a=2\(b-5)

.......................................

Hope you Bests!!!