Answer:
1. x= -2
2. -52
3. 12
4 x = 84
Step-by-step explanation:
sqrt( 3-2x) = sqrt( 1-3x)
Square each side
(sqrt( 3-2x))^2 = (sqrt( 1-3x))^2
3-2x = 1-3x
Add 3x to each side
3-2x+3x = 1-3x+3x
3+x = 1
Subtract 3 from each side
3+x-3 =1-3
x = -2
Check
sqrt( 3-2(-2)) = sqrt( 1-3(-2))
sqrt(3+4) = sqrt(1+6)
sqrt(7) = sqrt(7)
3/(x+7) = 4/(x-8)
Using cross products
3(x-8) = 4(x+7)
Distribute
3x-24 = 4x+28
Subtract 3x from each side
3x-3x-24 = 4x-3x+28
-24 = x+28
Subtract 28 from each side
-24 -28 =x+28-28
-52 =x
permutation notation P(n,r) = nPr = n!/(n-r)!
4P2 = 4!/ (4-2)! = 4*3*2*1/ 2*1 = 12
-6 log3 (x-3) = -24
Divide each side by -6
-6/-6 log3 (x-3) = -24/-6
log3( x-3) = 4
Raise each side to the base of 3
3 ^ log3( x-3) =3^ 4
x-3 = 81
Add 3 to each side
x-3+3 = 81+3
x = 84
