Question

|6x - 4| > 14?

Answer 1

\(\bf |6x - 4| > 14\implies
\begin{cases}
+(6x - 4) > 14\\ \quad \\
\bf -(6x - 4) > 14
\end{cases}\)

Answer 2

2 scenarios, 2 values for "x"

Answer 3

A. x > 3 or x < -5/3

B. x > 3 and x < 5/3

C. x < 3 or x > 5/3

D. x < 3 and x < 5/3

Answer 4

@jdoe0001 is ALMOST right... just one tiny mistake.
You put a negative sign to the quantity inside the absolute value, which makes the ENTIRE quantity of (6x + 4) negative.
\[14< \left(\begin{matrix}6x + 4 \\ -(6x+4)\end{matrix}\right)\]Let's do the top equation first.\[14 < 6x + 4\]\[10 < 6x\]\[x < \frac{ 10 }{ 6 } = \frac{ 5 }{ 3 }\]Now for the second equation:\[14 <-(6x + 4)\]\[14 < -6x - 4\]\[18 < -6x\]\[x > -3\] So the result is:\[x > \frac{ 5 }{ 3 }\] OR (it can't be both)\[x >-3\]

I don't know why it doesn't show up in your choices but that is the correct answer.

Answer 5

Wait. @jdoe0001 got it right. Sorry for calling you out. ^^;;