Irrational Numbers - SAT Subject Test in Math II

Card 0 of 1

Question

Define an operation $\vee$ on the set of real numbers as follows:

For any two real numbers ,

$a \vee b =\left | \left | a - 2b \right | + \left | 2a - b\right | \right |$ .

Evaluate $100 \vee\left ( -50 \right )$ .

Answer

Substitute in the expression:

$a \vee b =\left | \left | a - 2b \right | + \left | 2a - b\right | \right |$

$100 \vee (-50) =\left | \left | 100 - 2(-50)\right | + \left | 2 (100 ) - (-50)\right | \right |$

$=\left | \left | 100 - (-100)\right | + \left | 200 +50\right | \right |$

$=\left | \left | 200\right | + \left | 2 50\right | \right |$

$=\left | 200 + 2 50 \right |$

$=\left | 4 50 \right |$

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