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Answer 1 · 2016-05-11T14:01:52

k = #21/8# or #2.625#

We have
#2/3 + 8k/4 = 71/12#

Subtract 2/3 from both sides
#(2/3 - 2/3) + 8k/4 = 71/12 - 2/3#

Write 2/3 as 8/12 (multiply 4 in both numerator and denominator)

#8k/4 = 71/12 - 8/12#

Take #1/12# common

#8k/4 = (71-8)xx1/12#

Divide by 2 on both sides
#8k/(4xx2) = 1/2 xx 63/12#

You have
#cancel(8)k/cancel(8) = 63/24#

k = 63/24

Divide by both numerator and denominator by 3

#k = (63/3)/(24/3)#

#k = 21/8# or #2.625#