Question

How do you solve and check your solution given `-6=3/5a`?

Answer 1

See a solution process below:

Explanation:

Multiply each side of the equation by `color(red)(5)/color(blue)(3)` to solve for `a` while keeping the equation balanced:

`color(red)(5)/color(blue)(3) xx -6 = color(red)(5)/color(blue)(3) xx 3/5a`

`-30/color(blue)(3) = cancel(color(red)(5))/cancel(color(blue)(3)) xx color(blue)(cancel(color(black)(3)))/color(red)(cancel(color(black)(5)))a`

`-10 = a`

`a = -10`

To check the solution substitute `color(red)(-10)` for `color(red)(a)` in the original equation and calculate the result on the right side of the equation to ensure it equals `-6`

`-6 = 3/5color(red)(a)` becomes:

`-6 = 3/5 xx color(red)(-10)`

`-6 = 3/color(red)(cancel(color(black)(5))) xx cancel(color(red)(-10))-2`

`-6 = 3 xx -2`

`-6 = -6`

Therefore the solution is correct.