Chapter 1, Problem 17CR

To determine

To solve the given equation.

Answer to Problem 17CR

  $x=-1$

Explanation of Solution

Given:

Equation: $|x-2|=|4+x|$

Calculation:

Consider the given equation,

  $|x-2|=|4+x|$

Two equations can be written from an absolute equation.

  $(x-2)=-(4+x)\mathrm{..........}(i)$

Solving the equation,

  $\begin{array}{c}(x-2)=-(4+x)\\ x-2=-4-x\\ x-2+x=-4-x+x\\ 2x-2=-4\\ 2x-2+2=-4+2\\ 2x=-2\\ x=-1\end{array}$

  $(x-2)=(4+x)\mathrm{..........}(ii)$

Solving the equation,

  $\begin{array}{c}(x-2)=(4+x)\\ x-2=4+x\\ x-x=4+2\\ 0=6\end{array}$

The above expression is mathematically incorrect.

Conclusion:

Therefore, the solution to the given equation is $x=-1.$