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 < -\frac32`

On the other hand, if
`1-4x<0`, 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 < -\frac32\right) \cup (x > 2)`