What is the value of $k$ if $-\frac23(k-6) = \frac32(k+6)$?
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23/(k - 6) = 32/(k + 6)
Cross multiply:
23(k + 6) = 32(k - 6)
Distribute 23 and 32:
23k + 138 = 32k - 192
Subtract 23k to both sides:
138 = 9k - 192
Add 192 to both sides:
330 = 9k
Switch sides:
9k = 330
Divide both sides by 9:
k = 110/3
Answer: k = 110/3
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