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

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Answer 1 · 2014-12-12T20:31:33

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:

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

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

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

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

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

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

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

$-9/10 = -9/10$

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