Solving Inequalities Using Interval Notation and Set-Builder Notation

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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.

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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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