How do you solve #(2x-9)/4<=x+2# and graph the solution on a number line?

1 Answer
Jul 13, 2017

Answer:

#x ge -17/2#

Wolfram Alpha

Explanation:

Multiply both sides by #4#:

#(2x-9)/4 le x+2#

#4((2x-9)/4) le 4(x+2)#

#2x-9 le 4x+8#

Subtract #8# from both sides.

#2x-9-8 le 4x+8-8#

#2x - 17 le 4x#

Next, subtract #2x# from both sides.

#2x-17-2x le 4x - 2x#

#-17 le 2x#

Finally, divide both sides by 2.

#(-17)/2 le (2x)/2#

#-17/2 le x#

We can flip the inequality like this so it makes more sense:

#x ge -17/2#

Notice that the sign still points towards the bigger number (x). This inequality means that #x# is greater than #-17/2#, so to graph it on a number line, we will draw a solid dot on #-17/2# to indicate that #x# could be that number, and then shade in everything to the right of #-17/2#, since #x# can also be anything greater than it.

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Final Answer