What value of x satisfies both of the equations?

Instead of treating them as individual equations, use them as simultaneous equations.
|4x-7| = 5
|-8x+3| = 1

Now to get rid of the absolute value, square both sides of each equation.
(|4x-7|)² = 5 => 16x² - 56x + 49 = 25
(|-8x+3|)² = 1 => 64x² - 48x + 9 = 1

So our two equations are now
16x² - 56x + 49 = 25 => 16x² - 56x + 24 = 0
64x² - 48x + 9 = 1 => 64x² - 48x + 8 = 0

To use these as simlutaneous equations, we need to get the x² values equal, so we multiply the first equation by 4, and leave the second equation the same, giving
64x² - 224x + 96 = 0
64x² - 48x + 8 = 0

Now we subtract the second equation from the first, leaving us with one equation
( 64x² - 64x² = 0, -224x - (-48x) = -176x, 96 - 8 = 88 )
-176x + 88 = 0
-176x = -88
176x = 88
So x can only be equal to 1/2 :-)

1st equation:
4x - 7 = 5
4x = 12
x = 3

Answer: x = 3

2nd equation:
3 - 8x = 1
8x = 2
x = 1/4

Answer: x = 1/4

I don't see anything wrong with any of your conclusions.

3x+4y=-14 1 -6x-8y=28 (1 is multiplied by -2) + x+8y=-38 -5x=-10 x=2 x=2 3*2+4y=-14 y=-5 final results x=2 y=-5

if the parenthesis are absolute value, then

4x - 7 = -5 (1.a)
4x - 7 = 5 (1.b)


3 -8x = -1 (2.a)
3 -8x = 1 (2.b)

Solving from 1.a

4x - 7 = -5
4x = 2
x = 1/2 <-- this is the answer

from 2.a.
3 -8x = -1
-8x = -4
x = 1/2 <-- same with the one solved from 1.a

if you try to plug these in to the original equations, you'll find that they actually satisfy both the equations... so x = 1/2 is an answer...



from 1.b.
4x - 7 = 5
4x = 12
x = 3 <-- this is another possible answer

from 2.b
3 -8x = 1
-8x = -2
x = 1/4 <-- this is another possible answer

x = 3 and x = 1/4 don't satisfy both the equations,

so we're left with

x = 1/2 <-- this is the only value of x that will satisfy both equations.

the answer is x=1/2 because whenever ur dealing with absolute value problems there are two equations for example the absolute value of 4x-7=5 means 4x-7=5 and
4x-7=negative 5. its the samething for the other one so absolute value of 3-8x=1 means 3-8x=1 and 3-8x= negative 1
souse 4x-7=negative 5 wich makes x =1/2 an for 3-8x=negative 1 x=1/2 there u go

1)
|4x - 7| = 5
4x - 7 = ±5

4x - 7 = 5
4x = 5 + 7
4x = 12
x = 12/4
x = 3

4x - 7 = -5
4x = -5 + 7
4x = 2
x = 2/4
x = 1/2 (0.5)

∴ x = 1/2 (0.5) , 3

= = = = = = = =

2)
|3 - 8x| = 1
3 - 8x = ±1

3 - 8x = 1
-8x = 1 - 3
-8x = -2
x = -2/-8
x = 1/4 (0.25)

3 - 8x = -1
-8x = -1 - 3
-8x = -4
x = -4/-8
x = 1/2 (0.5)

∴ x = 1/4 (0.25) , 1/2 (0.5)

|4x-7| = 5 means 4x-7 = 5 or -5. So x = 3 or 1/2
Similarly |3-8x|=1 means x = 1/2 or 1/4
now you can find reqd value.