Question

Question #6cf09

Answer 1

See a solution process below:

Explanation:

First, multiply each side of the equation by `color(red)((2 - 7x^4))` to isolate the `z` term while keeping the equation balanced:

`15 xx color(red)((2 - 7x^4)) = (10z)/(2 - 7x^4) xx color(red)((2 - 7x^4))`

`15color(red)((2 - 7x^4)) = (10z)/color(red)(cancel(color(black)(2 - 7x^4))) xx cancel(color(red)((2 - 7x^4)))`

`15(2 - 7x^4) = 10z`

Now, divide each side of the equation by `color(red)(10)` to solve for `z` while keeping the equation balanced:

`(15(2 - 7x^4))/color(red)(10) = (10z)/color(red)(10)`

`((5 xx 3)(2 - 7x^4))/color(red)(5 xx 2) = (color(red)(cancel(color(black)(10)))z)/cancel(color(red)(10))`

`((color(red)(cancel(color(black)(5))) xx 3)(2 - 7x^4))/color(red)(color(black)(cancel(color(red)(5))) xx 2) = z`

`(3(2 - 7x^4))/2 = z`

`z = (3(2 - 7x^4))/2`

Or

`z = ((3 xx 2) - (3 xx 7x^4))/2`

`z = (6 - 21x^4)/2`

Or

`z = 6/2 - (21x^4)/2`

`z = 3 - (21x^4)/2`