Question

Absolute value inequality

Answer 1

Do I subtract the 6 first?

Answer 2

solve in between the brackets first

Answer 3

As in adding the 2?

Answer 4

subtract 6 from both sides, then multiply both sides by -1 (remember to flip the inequality) then tell me what you have

Answer 5

\[-abs(2x+2) \ge-3\]
Multiply by -1 gives all positive

Answer 6

So Abs(2x+2) ge 3

Answer 7

so now we have
\[6-|2x-2|\ge3\]subtract 6 from both sides\[-|2x-2|\ge-3\]
multiply by -1 and flip the sign
\[|2x-2|\le3\]
you with me now?

Answer 8

Whoops, forgot to flip. Yes.

Answer 9

Sorry man, I knew that.

Answer 10

\[|a|\le b \implies -b\le a\le b\]so
\[|2x-2|\le 3\]becomes\[-3\le 2x-2\le3\]add 2 to all three terms\[-1\le 2x\le5\]divide all terms by 2\[-\frac{1}{2}\le x\le\frac{5}{2}\]

Answer 11

this is the answer^^^

Answer 12

Thanks zzr0ck3r. Big time.

Answer 13

np, ask if you dont understand any of the steps

Answer 14

I do. I was adding the 2 too early.