How do you solve and graph #3/2x-7<2#?

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Answer 1 · 2017-09-03T13:25:58

See a solution process below:

First, add #color(red)(7)# to each side of the inequality to isolate the #x# term while keeping the inequality balanced:

#3/2x - 7 + color(red)(7) < 2 + color(red)(7)#

#3/2x - 0 < 9#

#3/2x < 9#

Now, multiply each side of the inequality by #color(red)(2)/color(blue)(3)# to solve for #x# while keeping the inequality balanced:

#color(red)(2)/color(blue)(3) xx 3/2x < color(red)(2)/color(blue)(3) xx 9#

#cancel(color(red)(2))/cancel(color(blue)(3)) xx color(blue)(cancel(color(black)(3)))/color(red)(cancel(color(black)(2)))x < 18/color(blue)(3)#

#x < 6#

To graph this we will draw a vertical line at #6# on the horizontal axis.

The line will be a dashed line because the inequality operator does not contain an "or equal to" clause.

We will shade to the left side of the line because the inequality operator contains a "less than" clause:

graph{x<6 [-10, 10, -5, 5]}