Greetings.
The answer is x = -2.
Explanation:
By solving the Absolute-Value Equation. We give them 2 conditions.
When x ≥ 0 and When x < 0
The different is that When x ≥ 0, |x-a| = x-a as defined.
And when x < 0. |x-a| = -x+a as defined.
( 1 ) - When x ≥ 0 for |x-1| and |x+5|
When x ≥ 0, |x-1| = x-1 and |x+5| = x+5
Therefore, x-1 = x+5
[tex]x-1=x+5\\x-x=5+1\\0=6[/tex]
Because the equation is false. Therefore, The condition (1) doesn't apply.
( 2 ) - When x ≥ 0 for |x-1| and x < 0 for |x+5|
This time, we try another condition.
When x ≥ 0, |x-1| = x-1 and When x < 0, |x+5| = -x-5.
[tex]x-1=-x-5\\x+x=-5+1\\2x=-4\\x=-\frac{4}{2}\\x=-2[/tex]
And we get the answer, |x-1| = |x+5| when x = -2.
But we haven't tried the last condition.
( 3 ) And that is when x < 0 for both terms.
|x-1| = -x+1 (x < 0)
|x+5| = -x-5 (x < 0)
[tex]-x+1=-x-5\\-x+x=-5-1\\0=-6[/tex]
The equation is not true. Therefore, the answer is x = -2.
