|4x-4|=|2x-7| Solve?

|4x - 4| = |2x - 7|
4x - 4 = 2x - 7
2x = - 3
x = - 3/2

|4x - 4| = - |2x - 7|
4x - 4 = - 2x + 7
6x = 11
x = 11/6

Answer: x = - 3/2, 11/6

The trick is to break one equation with a mod |y| sign into two - one with y and another with -y

4x-4=2x-7
2x = -3
x = -3/2

4-4x = 2x-7
x = 11/6

4x-4 = 7-2x
x = 11/6

4-4x = 7-2x
x = -3/2

x = -3/2, 11/6

because of the fact it extremely is already factored, you recognize that with a view to get 0 as an answer to the equation, between the climate ought to equivalent 0, so 4x-4=0 or 2x+7=0. From there, you remedy each of those equations for x. 4x-4=0 4x=4 (subtract -4 from the two sides of equation to isolate x) x=a million (divide the two sides via 4) 2x+7=0 2x=-7 x=-7/2 (comparable physique of suggestions as above) so x=a million or x=-7/2

|4x - 4| = |2x - 7|
+(4x - 4) = +(2x - 7) -- or -- +(4x - 4) = -(2x - 7)

+(4x - 4) = +(2x - 7)
4x - 2x = 4 - 7
2x = -3
x = -3/2 (-1.5)

+(4x - 4) = -(2x - 7)
4x - 4 = -2x + 7
4x + 2x = 4 + 7
6x = 11
x = 11/6

∴ x = -3/2 (-1.5), 11/6

oh right, this problem has 4 solutions:
|4x-4|=|2x-7|, first you equalize the equation to zero:

|4x-4|-|2x-7|=0
now, you have to take out the absolut values, therefore there are but 4 possibilities:
1. Both values are equal or higher than zero
(4x-4)-(2x-7)= 0
2x-3= 0
x=3/2

2. First value is lower than zero, and the second one is higher than zero
-(4x-4)-(2x-7)=0
-4x+4-2x+7=0
x=11/6

3. First value is higher than zero, and the second value is lower than zero
(4x-4)+(2x-7)=0
4x-4+2x-7=0
6x-11=0
x=11/6
4. First and second values are lower than zero
-(4x-4)+(2x-7)=0
-4x+4+2x-7=0
x=-3/2

1)4x-4=2x-7
2x=-3
x=-3/2
and
-4x+4=2x-7
-6x=-11
x=11/6,

|4x-4|=|2x-7|

4x - 4 = 2x - 7
2x = -3
x = -3/2