How do you solve #6x>=3+4(2x-1)#?

1 Answer
smendyka
Jul 1, 2017

See a solution process below:

Explanation:

First, expand the terms in parenthesis on the right side of the inequality so the common terms can be grouped and combined:

#6x >= 3 + color(red)(4)(2x - 1)#

#6x >= 3 + (color(red)(4) xx 2x) - (color(red)(4) xx 1)#

#6x >= 3 + 8x - 4#

#6x >= -4 + 3 + 8x#

#6x >= -1 + 8x#

Next, subtract #color(red)(8x)# from each side of the inequality to isolate the #x# term while keeping the inequality balanced:

#6x - color(red)(8x) >= -1 + 8x - color(red)(8x)#

#(6 - color(red)(8))x >= -1 + 0#

#-2x >= -1#

Now, divide each side of the inequality by #color(blue)(-2)# to solve for #x# while keeping the inequality balanced. However, because we are multiplying or dividing and inequality by a negative number we must reverse the inequality operator:

#(-2x)/color(blue)(-2) color(red)(<=) (-1)/color(blue)(-2)#

#(color(blue)(cancel(color(black)(-2)))x)/cancel(color(blue)(-2)) color(red)(<=) 1/2#

#x <= 1/2#

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