ExplanationThis function defines a made-up symbol: ~x is equivalent to |14x|. The question asks which statements must be true, so test each one:
~2 = ~(–2)
|14(2)| = |14(–2)|
|28| = |–28|
28 = 28
This first statement must be TRUE.Similarly, test the second statement:
~3 + ~4 = ~7
|14(3)| + |14(4)| = |14(7)|
42 + 56 = 98
98 = 98
This second statement must be TRUE.Finally, the third statement is also TRUE. Since ~x is equal to a statement inside an absolute value, this value can never be negative. If x = 0, then the value of |14x| is also 0. The minimum possible value for ~x is 0.
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