Question

Solve |1-4x| > 7 (x-1.5 (xlx < -1.5 UX>1.5) (xx<-1.5 UX > 2)

Answer 1

If $1-4x\ge0$, then by definition of absolute value

$|1-4x| = 1-4x > 7 \implies 4x < -6 \implies x < -\dfrac32$

On the other hand, if $1-4x$, then

$|1-4x| = -(1-4x) = -1 + 4x > 7 \implies 4x > 8 \implies x > 2$

So, the overall solution to the inequality is interval union

$\left(x < -\dfrac32\right) \cup (x > 2)$