How do you solve #-x + 7- 6x \geq 3( 6- 4x ) + 5x#?

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Answer 1 · 2017-03-11T18:48:31

See the entire solution process below:

FIrst, expand the terms within parenthesis on the right side of the inequality by multiplying each term within the parenthesis by #color(red)(3)#:

#-x + 7 - 6x >= color(red)(3)(6 - 4x) + 5x#

#-x + 7 - 6x >= (color(red)(3)xx6) - (color(red)(3)xx4x) + 5x#

#-x + 7 - 6x >= 18 - 12x + 5x#

Next, group and combine like terms on each side of the inequality:

#-1x - 6x + 7 >= 18 + 5x - 12x#

#(-1 - 6)x + 7 >= 18 + (5 - 12)x#

#-7x + 7 >= 18 - 7x#

Now, add #color(red)(7x)# to each side of the inequality:

#color(red)(7x) - 7x + 7 >= 18 - 7x + color(red)(7x)#

#0 + 7 >= 18 - 0#

#7 cancel(>=) 18#

Because #7# is not greater than #18# there is no solution to this problem for #x# or the solution is the null or empty set or #x = {O/}#