Question

X-8+3vx=y solve the literal equation for x

Answer 1

To solve the equation for x, X-8+3√x = y, we would follow these steps:

Step 1: Re-arrange the equation so that the term containing the square root of x is on one side. The equation then becomes: 3√x = y - x + 8

Step 2: Square both sides of the equation in order to eliminate the square root. You get:

(3^2) * (x) = (y - x + 8)^2

which simplifies to 9x = (y^2 - 2xy + y -64)

Step 3: Re-arrange the equation to make x the subject of the formula to get:
x = y^2/9 -2y/9 + y/9 -64/9

Step 4: It is important to note that squaring both sides of the equation can sometimes introduce extraneous solutions (solutions that are not actually solutions to the original equation). So, when you find a possible solution, you should always substitute it back into the original equation to verify that it is indeed a valid solution.

Hence, the two possible solutions for x given the equation X - 8 + 3√x = y are:
x = y - 3*sqrt(4*y + 41)/2 + 25/2

and

x = y + 3*sqrt(4*y + 41)/2 + 25/2

Answer 2

x =
`(y+8)/(1+3v)`

Explanation:

given

x - 8 + 3vx = y ( rearrange left side placing x- terms together )

x + 3vx - 8 = y ( add 8 to both sides )

x + 3vx - 8 + 8 = y + 8 ( simplify )

x + 3vx = y + 8 ← factor out x from each term on the left side

x(1 + 3v) = y + 8 ← divide both sides by 1 + 3v

`(x(1+3v))/(1+3v)` =
`(y+8)/(1+3v)` , then

x =
`(y+8)/(1+3v)`