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Algebraic Techniques, SM-Bank 030 MC

If \(\large x\) is a negative number, which of the following is true?

  1. \(x+2\)  is always negative.
  2. \(x\times -1\)  is always negative.
  3. \(2-x\)  is always negative.
  4. \(x-2\)  is always negative.
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\(D\)

Show Worked Solution

\(\text{Considering the options}\)

\(\text{Option 1: If}\ x\ge -2\ \text{then}\ x+2\ge 0, \therefore \text{not always negative}\)

\(\text{Option 2:}\ x\ \text{is negative }\therefore x\times -1\ \text{is always positive}\)

\(\text{Option 3:}\ x\ \text{is negative }\therefore 2-x\ \text{is always positive}\)

\(\text{Option 4:}\ x\ \text{is negative }\therefore x-2\ \text{is always negative}\)

\(\Rightarrow D\)