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Solving Inequalities Using Interval Notation and Set-Builder Notation

4(3w+4)greater than or equal to 4(2w+12), it says to put answers in interval notation,

that goes along with this one:

4-(3/2x-3)>1/2(x+5)

I am not sure how to sove either one of these, they are somewhat the same except the second question asks for the answer in set builder notation.

Solution Preview

Hi, here is the solution,

4 (3w +4) >= 4 ( 2w+12)

Use the distributive property,

{ a (b+c) = ab+ac }

So, 12w +16 >= 8w + 48

Isolate the variables and constants

12w -8w >= 48 -16

4w >= 32

Divide by 4 on both sides, we get

w>= 8

Interval notation [ 8, ...

Solution Summary

Inequalities are solved and expressed in interval and set builder notation. The solution is detailed and well presented.

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