If a number is doubled and then decreased by 6, which of the following expressions represents this operation?

If a number is doubled and then decreased by 6, which of the following expressions represents this operation?

• A. 2x - 6
• B. x - 6
• C. 2(x - 6)
• D. 2x + 6

Answer: (A)

To represent the operation of doubling a number and then decreasing it by 6, we start with a variable, typically denoted as \( x \). Doubling the number means multiplying it by 2, resulting in \( 2x \). Next, decreasing this result by 6 involves subtracting 6 from \( 2x \). Therefore, we can express this operation mathematically as \( 2x - 6 \). This expression accurately reflects the sequence of the operations—first doubling \( x \) and then performing a subtraction of 6. The other options do not align with the operations described in the question. For example, \( x - 6 \) only represents the subtraction without the doubling, \( 2(x - 6) \) indicates that 6 is subtracted first before doubling, and \( 2x + 6 \) suggests adding 6 after doubling, which is the opposite operation of what is required. Thus, the correct expression for the operation is \( 2x - 6 \).

To represent the operation of doubling a number and then decreasing it by 6, we start with a variable, typically denoted as ( x ). Doubling the number means multiplying it by 2, resulting in ( 2x ).

Next, decreasing this result by 6 involves subtracting 6 from ( 2x ). Therefore, we can express this operation mathematically as ( 2x - 6 ).

This expression accurately reflects the sequence of the operations—first doubling ( x ) and then performing a subtraction of 6. The other options do not align with the operations described in the question. For example, ( x - 6 ) only represents the subtraction without the doubling, ( 2(x - 6) ) indicates that 6 is subtracted first before doubling, and ( 2x + 6 ) suggests adding 6 after doubling, which is the opposite operation of what is required. Thus, the correct expression for the operation is ( 2x - 6 ).