madhan_dc wrote:Solve for x

1. 6> x+4 > 4

2. 2x > x+10 > -x

Hi,

when dealing with 3 part inequalities, here's the key rule to remember: whatever you do to one part, you must do to all 3 parts.

Since we're solving for x, we want to isolate x, i.e. strip the part of the inequality that contains x of everything except x itself.


1. 6> x+4 > 4

Here, to isolate x, we want to get rid of the "+4". To eliminate +4, we need to subtract 4 from that term. What we do to 1 term we must do to all 3 terms, so:

6 - 4 > x + 4 - 4 > 4 - 4

and

2 > x > 0

done!

2. 2x > x+10 > -x

This one is a bit more complicated, since there's no way to collect all of the Xs in the same part of the inequality. We can begin to simplify by adding x to each term:

2x + x > x + 10 + x > -x + x

3x > 2x + 10 > 0

Now, because we know that 3x > 0 (we can ignore the middle piece since the arrows all point in the same direction), we know that x > 0, i.e. x is positive. Since x is positive, 2x + 10 is greater than 0. Because the 2nd term is greater than the 3rd term, we can actually ignore that part of the inequality and just solve for:

3x > 2x + 10

Subtract 2x from both terms:

3x - 2x > 2x + 10 - 2x

x > 10

done!

Thanks guys!