Answer to Question #157290 in Calculus for Vishal

Question #157290

Show that there is real number x so that |x−1| = |x−2|.


1
Expert's answer
2021-01-21T19:13:03-0500

Function zeros:

x - 1 = 0; x - 2 = 0.

x = 1; x = 2.

Сases:

a) x "\\ge" 2

x - 1 = x - 2

x - x = 1 - 2

0x = -1. Not possible. No solutions.


b) x "\\ge" 1 and x < 2

"\\begin{cases}\n x \\in[1,2) \\\\\n x - 1 = -(x-2) \n\\end{cases}"

"\\begin{cases}\n x \\in[1,2) \\\\\n x - 1 = -x+2 \n\\end{cases}"

"\\begin{cases}\n x \\in[1,2) \\\\\n 2x = 3 \n\\end{cases}"

"\\begin{cases}\n x \\in[1,2) \\\\\n x = 1.5 \n\\end{cases}"

x = 1.5 - solution of this equation.


c) x < 1

-(x - 1) = - (x - 2)

-x + 1 = -x +2

-x + x = 2 -1

-0x = 1. Not possible. No solutions.

Answer: 1.5 - one solutions.



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