how to solve absolute value equation?

7 - 8* |7x-4| = -12

Take 7 over to the other side

- 8* |7x-4| = -19

Times both sides by -1

8* |7x-4| = 19

Divide both sides by 8

|7x-4| = 19/8

This basically means that 7x-4 is 19/8 from the origin. This means you need to solve the formular for the positive number that would make this true AND the negative number

Positive: 7x - 4 = 19/8

x = (19/8 +4)/7

x = 0.9107...

Now to get the other one set it equal to -19/8. This is because |-19/8| also equals 19/8

So..

7x - 4 = -19/8

x = (-19/8 + 4)/7

x = .232...

try to isolate the absolute value part and solve by using the two cases.

-8|7x - 4| = -19

|7x - 4| = 19/8

case 1 is where the answer is positive, so:

7x - 4 = 19/8

7x = 19/8 + 4

x = 51/56

case 2 is where the answer is negative, so:

7x - 4 = -19/8

7x = -19/8 + 4

x = 13/56

therefore, x = 51/56 or x = 13/56

7 - 8 |7x - 4| = -12

Subtract 7 from each side.

- 8 |7x - 4| = -19

Divide by -8.

|7x - 4| = 19/8

7x - 4 = -19/8 or 7x - 4 = 19/8

Add 4.

7x = 13/8 or 7x = 51/8

Divide by 7.

x = 13/56 or x = 51/56

there a 2 possibilties.....

|7x-4|= either -7x+4 or 7x-4 ok ...

now there will be two value of x :

7-8(-7x+4)= -12 7-8(7x-4)= -12

7+56x-32 = -12 7-56x+32 = -12

56x = 13 56x = 51

x=13/56 and x=51/56 :)

setup:

-8⎢7x - 4⎥ = -19

⎢7x - 4⎥ = 19/8

solution 1:

7x - 4 = 19/8

7x = 51/8

x = 51/56

solution 2:

7x - 4 = -19/8

7x = 13/8

x = 13/56

Hope this helps!

im not sure what an absolute value equation means, but to me it looks like calculus. you have to take the -8|7x-4| part and expand that. first you multiply -8 by 7x, then you multiply it by -4, which results in -56x+32. you then do 7-(-56x)+32=-12

7+56x+32=-12

56x=51

x=51/56

well, first you would multiply out the bracket to get 7-56x-32=-12 , then just solve the equation as you normally would

8+|x-1|=20 In any absolute value equation you MUST get rid of anything outside the absolute valu bars FIRST 8+|x-1|=20 -8...........-8 abs(x-1)=12.............since abs of 12 is 12 and the abs of -12 is 12 .......................you set what is in the absolute value bars equal to 12 and equal to -12 x-1=12...............x-1=-12............. add 1 to each side of both equations x=13..................x=-11