How do you solve and graph #7x-12<8#?

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Answer 1 · 2017-12-08T15:07:11

See a solution process below:

First, add #color(red)(12)# to each side of the inequality to isolate the #x# term while keeping the inequality balanced:

#7x - 12 + color(red)(12) < 8 + color(red)(12)#

#7x - 0 < 20#

#7x < 20#

Now, divide each side of the inequality by #color(red)(7)# to solve for #x# while keeping the inequality balanced:

#(7x)/color(red)(7) < 20/color(red)(7)#

#(color(red)(cancel(color(black)(7)))x)/cancel(color(red)(7)) < 20/7#

#x < 20/7#

Or

#x < 2.857# rounded to the nearest thousandth.

To graph this we will draw a vertical line at #20/7# 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 < 20/7 [-10, 10, -5, 5]}