Solve the equation | | 4x+1| | -4=4

Question

I dont understand this question at all

 

Answer 1

This is actually 2 equations in single expression.

mod P or |P| when P is an integer implies +P as well as -P

Thus ||4x+1||-4=4 gives + and - values of (4x+1) as well as + and - values of respective + and - values..

We can make adjustments to ||4x+1||-4=4

which implies, ||4x+1||=8 adding 4 to both sides

Hence we have,  |4x+1|=8 or -|4x+1|=8.....(1)

thus, either 4x+1=8...(2) or -(4x+1)=8 ... (3) OR multiplying both sides of (1) by -1 |4x+1|=-8

which implies, 4x+1=-8 .... (4) or -(4x+1)=-8...(5)

multiplying both sides of (4) by -1,  -(4x+1)=8 which is same as (3)

multiplying both sides of (5) by -1, (4x+1)=8 which is same as (2)

Thus, Subtracting 1 from both sides of (2), 4x=7

                                                        =>   x=7/4 .... Dividing both sides by 4

Again, Adjusting operators in (3), -4x-1=8
                                                =>-4x=9 ...........adding 1 to both sides

                                                =>   x=-9/4 .... Dividing both sides by -4

Hence the solution is x=7/4 or -9/4

                                                        =>   x=

Answer 2

I think you have used too may absolute value signs. I think it should read

|4x+1|-4 =4

|4x+1| =8

4x+1 =8   4x = 7   x= 7/4

 

 

or 4x+1 =-8   4x = -9   x= -9/4

 

answer: 7/4 and -9/4