Question

Solve the inequality: $|4x+5|-5>6$

Answer 1

Since $|x|=x$ and $-x$, therefore,

$|4x+5|-5>6$ may be calculated as:

$4x+5-5>6$ and $-(4x+5)-5>6$

$4x>6$ and $-4x-5-5>6$

$x>\frac{3}{2}$ and $-4x-10>6$

$x>\frac{3}{2}$ and $-4x>16$

$x>\frac{3}{2}$ and $x<-4$

That is $x$ lies between $(-\infty ,-4)\cup (\frac{3}{2},\infty )$.