How do you solve and graph #2x < 10# and #-5x <5#?

1 Answer
smendyka
Oct 23, 2017

See a solution process below:

Explanation:

To solve the first inequality, divide each side of the inequality by #color(red)(2)# to solve for #x# while keeping the inequality balanced:

#(2x)/color(red)(2) < 10/color(red)(2)#

#(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) < 5#

#x < 5#

To solve the second inequality, divide each side of the inequality by #color(blue)(-5)# to solve for #x# while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative term we must reverse the inequality operator:

#(-5x)/color(blue)(-5) color(red)(>) 5/color(blue)(-5)#

#(color(blue)(cancel(color(black)(-5)))x)/cancel(color(blue)(-5)) color(red)(>) -1#

#x > -1#

The solution is: #x > -1# and #x < 5#

Or, in interval notation: #(-1, 5)#

To graph this we will draw two vertical lines at #-1# and #5# on the horizontal axis.

The lines will be dashed lines because the inequality operators do not contain an "or equal to" clause.

We will shade between the interval of the lines:

enter image source here

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