Question

How to solve 8|x-11|+3 greater than or equal to 57

Answer 1

First isolate the absolute value expression:

`8|x-11|+3\ge57`

`8|x-11|\ge54`

`|x-11|\ge\frac{54}8=\frac{27}4`

Then by definition of absolute value,

• if
  `x\ge11`, then
  `|x-11|=x-11`, so the inequality reduces to
  `x-11\ge\frac{27}4` and we end up with
  `x\ge\frac{71}4`; otherwise,
• if
  `x<11`, then
  `|x-11|=-(x-11)=11-x`, so we have
  `11-x\ge\frac{27}4`, so
  `\frac{17}4\ge x`