Absolute Value Equations?

Question

1) |5x + 5| - 7 = 18

2) |4x - 2| = 10

Answer 1

remember |x| can be x and negative x

|5x+5| -7 = 18
add 7 both sides
|5x+5|= 25
so 5x+5 = 25 or 5x+5= -25
5x= 20 (subtract 5 both sides) or 5x = -30 (subtract 5 both )
divie 5 both sides for both equations
x = 4 or x = -6

2.

|4x - 2| = 10

4x-2 = 10 ...................... 0r 4x -2 = -10
add 2 for both sides of 2 equations

4x= 12 .................. or 4x = -8

divide 4 both sides for both 2 equations

x = 3 and x = -2

P/S the the third person's answer is wrong x= 0, and x = -10
if you plugged it back to original function that will give the error
check x = 0
|5*0+5| -7 =18
|5| -7= 18
5-7=18
-2 = 18 (no way)

vlee125 please edit your answer

Answer 2

|x| = x if x≥0 ; |x|= -x if x<0. Then:

1) |5x + 5| - 7 = 18 is :

* If 5x+5≥0 ( --> x≥-1) 5x+5-7=18 ; 5x=20 --> x=4
* If 5x+5<0 (--> x<-1) -5x-5-7=18; -5x=30 --> x=-6

2) |4x - 2| = 10

* If 4x-2 ≥0 ( --> x≥ 1/2) 4x-2=10 --> x=3
* If 4x-2<0 (--> x<1/2) -4x+2=10 --> x=-2

Saludos.

Answer 3

1) |5x + 5| - 7 = 18
5|x+5| = 18 + 7 = 25
| x + 5| = 5
i) x + 5 >=0
x + 5 = 5 or x = 0
ii) x + 5 < 0
-x - 5 = 5
-x = 10
x = - 10
Ans x = 0 or x = -10

2) |4x - 2| = 10
2 | 2x - 1| = 10
| 2x - 1| = 5
i) 2x -1 >=0
2x -1 = 5
2x = 6
x =3
ii) 2x - 1 < 0
1 - 2x = 5
2x = - 4
x = -2

Ans x = 3 or x = - 2

Answer 4

Rearrange your equations so that the stuff inside the absolute value bars is on the left and the remainder is on the right.

Now all you have to do is throw away the absolute value sign and solve the equation twice. Once, assuming a positive value on the right side, and a second time assuming a negative value on the right side.

For the second one you need to solve
4x - 2 = 10
and also
4x - 2 = -10

Usually, but not always, you will end up with two different values for x