Inequality word problem

One more problem. My son missed this problem and doesn't understand why.

Problem: The middleweight division is centered at 160 pounds. Deviation from that must be three pounds in either direction. Write an inequality for that weight, W.

My wrong answer: l x-3 l is less than or equal to 160.

Thanks.

toneymom said:

One more problem. My son missed this problem and doesn't understand why.

Problem: The middleweight division is centered at 160 pounds. Deviation from that must be three pounds in either direction. Write an inequality for that weight, W.

My wrong answer: l x-3 l is less than or equal to 160.

Your variable should be "W" - not 'x'. The inequality should be

157 ? W ? 163

Thanks.

Click to expand...

Let us figure out what his answer mean:

|W - 3| ? 160

then

W - 3 ? 160..............................OR .............................. -(W-3) ? 160

W ? 163 .................................OR ................................-W ? 157 .....................W ? -157

So his answer translates to

-157 ? W ? 163

With absolute value notation - his expression should be:

|W - 160| ? 3

I figured it out and got the right answer. Here's how we did it.

l 160-w l < or equal to 3

so...

160 - w < 3 160 - w > -3
-w < -157 - w > -163
w > 157 w < 163

*these should be or equal to but I couldn't figure out how to underline them.

Your work is correct.

On a different note, if you have MS keyboard - then typing <ALT>243 (with numlock on - pressing ALT key - while typing 243 on numeric key pad) will display ? and <ALT>242 will display ?

Thanks for the info!