Help! Algebra math Question!!?

Question

Okay...this problem has me 100% lost...

-3/5 < 1/5 - 2/5w < -1/3

I'm supposed to "solve the compound inequality and state the solution set in interval notation" and I've got noooo clue where to even start. Anyone out there??

Answer 1

First, isolate the variable by subracting 1/5 from the center. Sooo, it'll be like this:

-2/5 < -2/5w < -8/15

Then, divide the middle by -2/5, and remember to flip the signs:

1 > w > -4/3

...That's your answer :)

That means that w can be any number between 1 and -4/3.

Answer 2

Start by cleaning up the fractions; multiply everything by 15 to get: -9 < 3 - 6w < -5. Subtract 3 to clean up the innards, getting -12 < -6w < -8. Negate everything to give w a positive coefficient: 12 > 6w > 8. Finally, divide by 6 to get w alone: 2 > w > 4/3. And you can finish the job.

Answer 3

-3/5 < 1/5 - 2/5w < -1/3
Multiply by 5 to get rid of some fractions getting:
-3 < 1 -2w < -5/3
Multiply by -1 and change < to > getting:
3 > -1 +2w > 5/3
Add 1 to all terms to get rid of the -1 in the middle term, getting:
4 > 2w > 8/3
Divide by 2 getting:
2> w> 4/3
If you plotted 4/3 and 2 on a number line, w would be any number between them.

Answer 4

1st, convert to a common denominator:
-9/15 < 3/15 - 6/15w < -5/15
Then multiply each part of the inequality by that denominator to get rid of it:
15*(-9/15) < 15*(3/15) - 15*(6/15)w < 15*(-5/15) which leaves:
-9 < 3 - 6w < -5
Now subtract 3 from each part of the inequality to isolate 6w:
-9 - 3 < 3 - 6w - 3 < -5 - 3 which leaves:
-12 < -6w < -8
Since every part of the inequality is negative, you can make each part positive, and switch the signs:
12 > 6w > 8
Finally divide each part of the inequality by 6 to get w:
12/6 > 6w/6 > 8/6 which leaves:
2 > w > 4/3

Answer 5

im not sure between these two:

2 0.8