How do you solve #\frac { 1} { 7} r + \frac { 53} { 56} > \frac { 6} { 7}#?

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Answer 1 · 2016-12-04T14:34:56

#r > -5/8#

First, change each constant to have the same common denominator, in this case 56, by multiplying it by the correct for of #1# if necessary:

#1/7r + 53/56 > (8/8)*(6/7)#

#1/7r + 53/56 > 48/56#

Now we can solve for #r# using the necessary mathematics while keeping the inequality balanced:

#1/7r + 53/56 - 53/56 > 48/56 - 53/56#

#1/7r + 0 > -5/56#

#1/7r > -5/56#

#7 * 1/7r > 7 * -5/56#

#r > 7 * -5/(8*7)#

#r > cancel(7) * -5/(8*cancel(7))#

#r > -5/8#