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mariarad [96]
2 years ago
15

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

Mathematics
1 answer:
Setler [38]2 years ago
3 0

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)

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