plz help! inequalities

[jamin123]

I have two problems on my Algebra 2 homework that I don't understand. Plz help!

Write an absolute value ineqaulity for each compound inequality.

1) w -is greater than or equal to- 12 OR w -is lesser than or equal to- -2


2) -10 -is lesser than- x -lesser than- -2

 

[arthur ohlsten]

1)
w<=2 or w>=12
indicate these expressions by drawing vertical lines at w=2 and w=12
draw diagonal lines below w=2 and above w=12 this is the area of interest
the midpoint of the w line is w=[2+12]/2 w=7
plot l w-7l for w between 2 and 12 at w=2 the amplitude is 5
at w=12 the amplitude is 5
the area of interest is l w-7l>= 5 answer

2) lx+6l <4 you do it by the same method

Arthur

 

[wjm11]

1) w -is greater than or equal to- 12 OR w -is lesser than or equal to- -2

I think Arthur may have misread that final "2" as positive rather than negative. Regardless, use his method:

The avg of 12 and -2 is (12 + (-2))/2 = 5

plot y = l w-5l for w between -2 and 12

The amplitude (y value) at both -2 and 12 is 7

Final inequality: l w-5l >= 7