Question #5a2c1

1 Answer
seph
Nov 8, 2015

#x = -11#

Explanation:

#6 - 2(5 -2x)^(2/3) = -12#

First, we simplify the equation as much we can

#=> -2(5 -2x)^(2/3) = -18#

#=> (5 - 2x)^(2/3) = -18/-2#

#=> (5 - 2x)^(2/3) = 9#

Next we remove the fractional exponent by raising both sides of the equation by a power that will make the resulting exponent a whole number, preferably 1. In this case, let's raise both sides of the equation by #3/2#

#=> [(5 - 2x)^(2/3)]^(3/2) = 9^(3/2)#

#=> 5 -2x = (3^2)^(3/2)#

Now that #x#'s exponent have been removed, we can proceed to solving for #x#

#=> 5 - 2x = 3^3#

#=> 5 - 2x = 27#

#=> -2x = 22#

#=> x = -11#

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