How do you solve #2( 3x - 5) < 4#?

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Answer 1 · 2017-05-11T23:38:15

See a solution process below:

First, divide each side of the inequality by #color(red)(2)# to eliminate the parenthesis while keeping the inequality balanced:

#(2(3x - 5))/color(red)(2) < 4/color(red)(2)#

#(color(red)(cancel(color(black)(2)))(3x - 5))/cancel(color(red)(2)) < 2#

#3x - 5 < 2#

Next, add #color(red)(5)# to each side of the inequality to isolate the #x# term while keeping the inequality balanced:

#3x - 5 + color(red)(5) < 2 + color(red)(5)#

#3x - 0 < 7#

#3x < 7#

Now, divide each side of the inequality by #color(red)(3)# to solve for #x# while keeping the inequality balanced:

#(3x)/color(red)(3) < 7/color(red)(3)#

#(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) < 7/3#

#x < 7/3#