Question

What is the inequality?
4|2w+3|-7<9
I know the answer is 3.5 12 years ago

Answer 1

To solve the inequality, you have to isolate the expression within the absolute value symbol first

Answer 2

But what does that mean?

Answer 3

You have to get the \[\left|2w+3? \right|\] by itself

Answer 4

\[\left| 2w+3 \right|\]

Answer 5

I've been doing that but it comes out as w<4.5 instead of w<3.5

Answer 6

Could you show your work?

Answer 7

Sure, And I actually meant it's suppose to be w<-3.5

Answer 8

4|2w+3|-7<9
|2w+3|-3<9

-Add 3 to both sides-
2w+3<12

-Subtract 3-

2w<9

w<4.5

And I try to solve it different every time but it still doesn't come out right.

Answer 9

And I did this way too.
4|2w+3|-7<9
-9<4(2w+3)-7<9
-9<8w+12-7<9

Add 5

-14<8w<4

Divide 8

-7/4<w<1\2

Answer 10

I think what you're trying to do is combine the 4 and the -7, which you can't do since the 4 is the coefficient of the absolute value

Answer 11

So are you saying I need to do distributive property? Because I did that in the second one.

Answer 12

This is how the problem should be worked out.
\[4\left| 2w+3 \right|-7<9\]
\[4\left| 2w+3 \right|<16\] we added the 7 to both sides
\[\left| 2w+3 \right|<4\] divided both sides by 4
Now we set up 2 inequalities
\[2w+3<4\] \[2w+3>-4\]

Answer 13

and is the answer really 3.5<w<.5
or did you mean to put -3.5<w<.5

Answer 14

Yeah, I added earlier that I mean -3.5. Thank you so much! That makes a lot more sense now!

Answer 15

You're welcome.