How do you solve #2x + 17< \frac { 3( 1- 5x ) } { - 7}#?

1 Answer
smendyka
Nov 20, 2016

#x > 122#

Explanation:

To complete this problem you want to isolate and solve for #x# while always keeping the inequality balanced:

First, multiple each side of the equation by #-7# to remove the fraction. Remember, multiplying or dividing by a negative number reverse the inequality:

#-7(2x + 17) > (-7(3(1 - 5x)))/-7#

#-7(2x + 17) > 3(1 - 5x)#

Next, expand the terms in parenthesis on each side of the inequality:

#(-7*2x) + (-7*17) > (3*1) + (3*-5x)#

#-14x - 119 > 3 - 15x#

Now, we can add #119# to each side of the inequality:

#-14x - 119 + 119 > 3 + 119 - 15x#

#-14x > 122 - 15x#

Finally we can add #15x# to each side of the inequality:

#15x - 14x > 122 - 15x + 15x#

#(15 - 14)x > 122#

#1x > 122#

#x > 122#

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