How do you solve #\frac { x + 6} { 3} \geq x - 2#?

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Answer 1 · 2017-06-22T06:21:43

#x<=6#

Thankfully, solving inequalities is almost exactly the same as solving equations! We can approach this problem the same way.

#(x+6)/3>=x-2#

First, start off by multiplying #3# on both sides.

#3/1*(x+6)/3>=3(x-2)#

This will cancel out the #3# on one side.

#cancel3/1*(x+6)/cancel3>=3(x-2)#

#x+6>=3(x-2)#

Use the distributive property to simplify the right side of the inequality.

#x+6>=3x-6#

Subtract #x# on both sides to bring all variable terms to the right side.

#6>=2x-6#

Add #6# to both sides to bring all constants to the left side.

#12>=2x#

Last, divide by #2# to completely isolate #x#.

#6>=x#

Don't forget to rewrite your inequality in the correct order! You've finally arrived to your answer:

#x<=6#