Identify \(\text{every}~\text{representation}\) with the same algebraic structure as \(\text{twice}\) the grouped quantity \(x\) minus \(3\), or \(2(x~-~3)\). Report the complete set of labels.
Representations:
A. \(2(x~-~3)\)
B. \(2x~-~3\)
C. \(x~-~6\)
D. the difference of \(2x\) and \(3\)
E. \(\text{two}~\text{times}\) the result of subtracting \(3\) from \(x\)
F. \(3~-~2x\)
G. the product of \(2\) and the quantity \(x~-~3\)
H. subtract \(3\) from the product of \(2\) and \(x\)
What this problem is really about
Fix the target structure before checking the representations: subtract three from x first, then multiply that entire result by two. For each symbolic or verbal form, track grouping and operation order rather than merely noticing the same numbers and variable. Report every label that preserves both the inner difference and the outside multiplier.