1 Answer

Munsifali · Answer 1 · 2023-06-14T14:06:50+0000

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

$\left(x < -\frac32\right) \cup (x > 2)$

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