Math help, (Algebra) ! I really don't get this! Full points!

Hi,
Thank you for viewing my question it means a lot! I just got some test results back and got these two problems wrong I know the answers, but don't know how to get there.
1) (4x+3)^5-17=15
answer: -1/4

2) -3 I4x-9I>=-45
the answer should be 6>=x>=-1.5

I have a test tomorrow on these topics and the steps on either one would help so much! I really appreciate it!

(4x+3)^5-17=15

(4x+3)^5 = 32

(4x+3)^5 = 2^5

4x + 3 = 2

4x = -1

x = -1/4





-3 I4x-9I >= -45

I4x-9I <= 15

but I4x-9I = 4x-9 if 4x-9>0 or 4x>9 or x > 2.25---------[1]
I4x-9I = -(4x-9) if 4x-9<0 or x < 2.25-------------[2]

in first case 4x-9 <= 15
4x <=24
x <= 6-----------------------[3]

in second case -(4x-9)<=15
-4x <=6
x <= -1.5-------------------[4]

from 3 and 4

6>=x>=-1.5

1) (4x+3)^5-17=15

Isolate the variable expression by adding 17 to both sides: (4x+3)^5 = 32
Now remove ( ) by finding 5th root of both sides: 4x+3 = 2, since 2^5 = 32.
Subtract 3: 4x = -1
Divide by 4: x = -1/4


2) -3 I4x-9I>=-45

Isolate the variable expression by dividing by -3, remembering the inequality reverses when you / or * by a negative: I4x-9I <= 15
Now set up two inequalities: I4x-9I <= 15 means -15<=4x-9<=15, so your two sentences are
-15<=4x-9 and 4x-9<=15.
Solve each sentence: -15<=4x-9 -> -6<=4x (add 9) -> -1.5<=x (divide by 4)
and 4x-9<=15 -> 4x<=24 (add 9) -> x<=6 (divide by 4)
Combine your two inequalities: -1.5<=x<=6, or 6>=x>=-1.5

1) (4x+3)^5=32 {2^5=32}
hence 4x+3=2
x=-1/4

2) |4x-9|<=45/3 {coz when u multiply 2 sides by minus inequality reversed eg 2<3 but-2>-3}
now make cases
case 1: 4x-9>=0 4x-9<=15 x<=6
from this case 9/4= case 2: 4x-9<0 9-4x<=15 x>=1.5
from this case -1.5=
combine both cases 2 get ans

Q1.
(4x+3)^5 -17=15
(4x+3)^5=32
(4x+3)^5=(2)^5
4x+3=2
4x=-1
x=-1/4

Q2.
-3|4x-9|>= -45
|4x-9|<=15

Case1: if (4x-9)>=0
4x-9<=15
4x<=24
x<=6

Case2: if (4x-9)<0
-(4x-9)<=15
-4x+9<=15
4x>= -6
x>= -1.5

hence, -1.5<=x<=6