Twice a number decreased by 6. Write a mathematical expression for the sentence above and also an equivalent expression for it.

Question

2x - 6 = 2x - 3
2x - 6 = 2(x - 3)
2x - 6 = x - 3
2x - 6 = 2(x - 6)

Answer 1

The phrase "Twice a number decreased by 6" can be represented mathematically as:

Expression: \( 2x - 6 \)

where \( x \) is the number.

Now, let's evaluate the equivalent expressions provided:

1. \( 2x - 6 = 2x - 3 \) (not equivalent)
2. \( 2x - 6 = 2(x - 3) \) (equivalent, since \( 2(x - 3) = 2x - 6 \))
3. \( 2x - 6 = x - 3 \) (not equivalent)
4. \( 2x - 6 = 2(x - 6) \) (not equivalent)

Summary: The equivalent expression for "Twice a number decreased by 6" is \( 2(x - 3) \).