The sentence "Twice a number decreased by 6" can be represented mathematically as \( 2x - 6 \).
Now, we need to determine which of the provided options represent equivalent expressions.
The original expression is: \[ 2x - 6 \]
Let's analyze the options:
a. \( 2x - 6 = 2x - 3 \)
This is not equivalent, as \( -6 \) is not equal to \( -3 \).
b. \( 2x - 6 = 2(x - 3) \)
Expanding the right side gives \( 2x - 6 \), so this is equivalent.
c. \( 2x - 6 = x - 3 \)
This is not equivalent, as \( 2x \) does not equal \( x \).
d. \( 2x - 6 = 2(x - 6) \)
Expanding the right side gives \( 2x - 12 \), so this is not equivalent.
The only equivalent expression is option b: \( 2x - 6 = 2(x - 3) \).