Chapter ISG, Problem 3.8.8P

To determine

To calculate the given equation

Answer to Problem 3.8.8P

The set of solution for the given equation is,

{-1, 11}

Explanation of Solution

Given information:

The equation is,

  $8-\left|5-x\right|=2\left|5-x\right|-10$

Formula used:

Equation solving.

Calculation:

Shifting left hand side values to right hand side,

  $2\left|5-x\right|+\left|5-x\right|=8+10$

So,

  $3\left|3-x\right|=18$

Cross-multiplying,

  $\left|5-x\right|=\frac{18}{3}$

On solving,

  $\left|5-x\right|=6$

Opening mod,

  $5-x=\pm 6$

Shifting the left hand side values to right hand side,

  $-x=\pm 6-5$

If +6,

  $-x=6-5$

On solving,

  $x=-1$

If -6,

  $-x=-6-5$

On solving,

  $x=11$

Hence the set of solution for the given equation is,

{-1, 11}