Final answer:
The phrase 'twice the difference of a number and 3' translates to the algebraic expression 2(x - 3), where 'x' represents the number.
Step-by-step explanation:
Translating Words to Algebraic Expressions
To translate the phrase 'twice the difference of a number and 3' into an algebraic expression, you first identify the operations involved. The word 'difference' implies subtraction, and the word 'twice' implies multiplication by two. Let's define the variable 'x' to represent the number in question. The difference of 'x' and 3 is expressed as 'x - 3'. Therefore, to represent 'twice' this difference, we multiply the whole expression by 2. This gives us 2(x - 3) as the final algebraic expression.