Which shows how to insert parentheses to make the statement true? \( \begin{array}{l}12-3 \times 2+6=24 \\ (12-3) \times 2+6=24 \\ 12-(3 \times 2)+6=24 \\ 12-3 \times(2+6)=24 \\ 12-(3 \times 2+6)=24\end{array} \)
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Let's evaluate each option to see if parentheses can be inserted to make any of the statements true. 1. \( (12-3) \times 2+6 \): - First calculate \( 12-3 = 9 \) - Then, \( 9 \times 2 = 18 \) - Finally, \( 18 + 6 = 24 \) (This one works!) 2. \( 12-(3 \times 2)+6 \): - Calculate \( 3 \times 2 = 6 \) - Then, \( 12 - 6 + 6 = 12 \) (Does not work) 3. \( 12-3 \times(2+6) \): - Calculate \( 2 + 6 = 8 \) - Then, \( 3 \times 8 = 24 \) - Now, \( 12 - 24 = -12\) (Does not work) 4. \( 12-(3 \times 2+6) \): - Calculate \( 3 \times 2 = 6 \) - Then, observe \( 6 + 6 = 12 \) - Finally, \( 12 - 12 = 0 \) (Does not work) The only valid option is: \[ (12-3) \times 2+6=24 \]