How do you solve and graph #5-5x>4(3-x)#?

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Answer 1 · 2017-07-02T01:00:05

See a solution process below:

First, expand the terms on the right side of the inequality by multiplying the terms inside the parenthesis by the term outside the parenthesis:

#5 - 5x > color(red)(4)(3 - x)#

#5 - 5x > (color(red)(4) xx 3) - (color(red)(4) xx x)#

#5 - 5x > 12 - 4x#

Next, add #color(red)(5x)# and subtract #color(blue)(12)# from each side of the inequality to solve for #x# while keeping the inequality balanced:

#-color(blue)(12) + 5 - 5x + color(red)(5x) > -color(blue)(12) + 12 - 4x + color(red)(5x)#

#-7 - 0 > 0 + (-4 + color(red)(5))x#

#-7 > 1x#

#-7 > x#

To state the solution in terms of #x# we can reverse or "flip" the entire inequality:

#x < -7#