solve the absolute value inequalities write the soultion in

solve the absolute value inequalities. write the soultion in interval notation. (a) 2abs(x+4)+3<13 (b) -3abs(x+5)+18 smaller than or equal to 15

a) 2|x+4| +3 <13

for x+4> 0 : 2(x+4) +3 <13

2x+8 +3 < 13 ----> x <1

x+4<0 ; -2(x+4) +3< 13

2(x+4)>-10 ----> x>-9

So, solution : -9<x <1

b) -3|x+5|+18 <= 15

for (x+5) >0 : -3(x+5) +18 <=15

-3(x+5)<=-3

x+5 >=1 ---> x >= -4

for (x+5)<0 : 3(x+5) + 18 <=15

x+5<=-1

x<=-6

Solution :x<=-6 or x >=-4