Question

Determine whether the statement is sometimes, always, or never true. Explain your reasoning.
If A and B are realnumbers, then negative times absolute value of a plus 2 times b is negative

Answer 1

always
negative times the absolute value of anything is negative.

Answer 2

If you mean:
\[-\left| A \right| + 2*B < 0\]
Then it is sometimes true, some examples:
A = 1, B = 2
\[-(1) + 2*(2) = 3\] which of course is not negative, so in this case is false
or
A = 5, B = 1
\[-(5)+2*(1) = -3\] which is negative and in this case is true.

Answer 3

the whole thing is absolute value

Answer 4

In that case, mfleisch5's answer is bang on.