How do you solve and graph #7n - 1 < 3n + 5#?

1 Answer
May 17, 2018

Answer:

See a solution process below:

Explanation:

First, add #color(red)(1)# and subtract #color(blue)(3n)# from each side of the inequality to isolate the #n# term while keeping the equation balanced:

#7n - color(blue)(3n) - 1 + color(red)(1) < 3n - color(blue)(3n) + 5 + color(red)(1)#

#(7 - color(blue)(3))n - 0 < 0 + 6#

#4n < 6#

Now, divide each side of the inequality by #color(red)(4)# to solve for #n# while keeping the inequality balanced:

#(4n)/color(red)(4) < 6/color(red)(4)#

#(color(red)(cancel(color(black)(4)))n)/cancel(color(red)(4)) < 3/2#

#n < 3/2#

To graph this on a number line we put a hollow circle at #3/2#. The circle is hollow because there is no "or equality to" clause in the inequality operator.

We draw a line from #3/2# to the left because the inequality operator is a "less than" clause.

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