Question

How do you solve for r in `- \frac{59}{60} = \frac{1}{6} \(- \frac{4}{3} r-5 )`?

Answer 1

Answer: `r = 27/40`

Explanation:
We start with our equation:

`-59/60 = 1/6(-4/3r - 5)`

We can now multiply both sides of the equation by `6`:

`(-59* 6)/60 = -4/3r - 5`

We notice that `60 = 6*10` so we can cancel out the `6` on the left hand side:

`(-59*6)/(10*6) = -4/3r - 5`

`-59/10 = -4/3r - 5`

Now we can add `5` to both sides to further isolate r:

`-59/10 + 5 = -4/3r - 5 + 5`

`-59/10 + 50/10 = -4/3r`

`-9/10 = -4/3r`

And then multiply both sides by `3/4` to get the value of r:

`-9/10*-3/4 = -4/3r*-3/4`

`-9/10*-3/4 = r`

`27/40 = r`

`r = 27/40`

Checking work:

`-59/60 = 1/6(-4/3r - 5)`

`-59/60 = 1/6(-4/3*27/40 - 5)`

`-59/60 = 1/6(-108/120 - 5)`

`-59/60 = 1/6(-27/30 - 5)`

`-59/10 = (-27/30 - 5)`

`-59/10 + 5 = -27/30`

`(-59 + 50)/10 = -9/10`

`-9/10 = -9/10`