Question

How do you solve `1/2z+1/3=-2/5`?

Answer 1

See the entire solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(30)` to eliminate the fractions while keeping the equation balanced. `color(red)(3)` is the Lowest Common Denominator of the three fractions:

`color(red)(30)(1/2z + 1/3) = color(red)(30) * -2/5`

`(color(red)(30) * 1/2z) + (color(red)(30) * 1/3) = cancel(color(red)(30))6 * -2/color(red)(cancel(color(black)(5)))`

`(cancel(color(red)(30)) 15 * 1/color(red)(cancel(color(black)(2)))z) + (cancel(color(red)(30)) 10 * 1/color(red)(cancel(color(black)(3)))) = 6 * -2`

`(15 * 1z) + (10 * 1) = -12`

`15z + 10 = -12`

Next, subtract `color(red)(10)` from each side of the equation to isolate the `z` term while keeping the equation balanced:

`15z + 10 - color(red)(10) = -12 - color(red)(10)`

`15z + 0 = -22`

`15z = -22`

Now, divide each side of the equation by `color(red)(15)` to solve for `z` while keeping the equation balanced:

`(15z)/color(red)(15) = -22/color(red)(15)`

`(color(red)(cancel(color(black)(15)))z)/cancel(color(red)(15)) = -22/15`

`z = -22/15`

Answer 2

`z=-22/15`

Explanation:

First, let's multiply all terms by 30 to remove the fractions.
Doing this, we get:
`15z+10=-12`

Then, we simplify.
`15z=-22`

`z=-22/15`