What are the solutions to |3x - 4| = 11?

An absolute value equation splits into two cases. If $3x-4=11$, then $3x=15$ and $x=5$. If $3x-4=-11$, then $3x=-7$ and $x=-\frac{7}{3}$. So the solutions are $5$ and $-\frac{7}{3}$, choice F. Choice G has $+\frac{7}{3}$, which drops the negative sign: $|3(\frac73)-4|=3$, not $11$. Choice H gives $-5$, which fails because $|3(-5)-4|=19$. Choice J finds only one solution and misses the negative case. An equation $|A|=11$ always has two solutions when the right side is positive.