Solve for x. x- |2x-1| =7?

x- |2x-1| =7 ==> x - 7 = |2x-1|.

So, x - 7 = 2x-1 or x - 7 = -(2x-1)
==> x - 7 = 2x-1 or x - 7 = -2x+1
==> -7 = x-1 or 3x - 7 = 1
==> -6 = x or 3x = 8
==> x = -6 or 8/3.

Double checking the answers, we see that x = -6 and x = 8/3 are both extraneous solutions.

Final answer: No solution!

x - |2x - 1| = 7
- 2x + 1 = 7 - x
x = - 6

x - |2x - 1| = 7
- |2x - 1| = x - 7
- 2x + 1 = x - 7
3x = 8
x = 8/3

Answer: x = - 6, 8/3

x - |2x - 1| = 7
|2x - 1| = x - 7
2x - 1 = ±(x - 7)

2x - 1 = x - 7
2x - x = 1 - 7
x = -6

2x - 1 = -(x - 7)
2x - 1 = -x + 7
2x + x = 1 + 7
x = 8/3

∴ x = -6, 8/3

x-7=|2x-1|

(x-7)^2 =(|2x-1|)^2

x^2-14x+49=4x^2-4x+1

3X^2+10X-48=0

[X - (23/6)][x+(26/6)]=0

Therefor

X=3.833 and X=-4.333
BUT non of these will not satisfy the equation.

SO my answer is there are no solutions.

2x-1 = 0 when 2x = 1 or x = 1/2
Take the following two cases.

Case: x >= 1/2
2x - 1 >= 0
|2x-1| = 2x-1

x- |2x-1| =7
x - (2x-1) = 7
x - 2x + 1 = 7
-x + 1 = 7
-x = 6
x = -6
But x = -6 violates the condition x > 1/2 of this case. Therefore x = -6 is rejected.

Case: x < 1/2
2x - 1 < 0
|2x - 1| = -(2x - 1) = 1 - 2x

x - |2x - 1| = 7
x - (1 - 2x) = 7
x - 1 + 2x = 7
3x - 1 = 7
3x = 8
x = 8/3
This is also rejected because x=8/3 violates the condition x < 1/2 of this case.

Ans: There is no solution

x-(-2x+1)=7
3x-1=7
x=2
&
x-(2x-1)=7
-x=6
x=-6
You must solve TWO equations.

x=-8

x-2x+1=7
-x=6
x=-6
x+2x-1=7
3x=8
x=8/3