Which of the following is an arrangement of the four basic arithmetic operation signs so that when the signs are placed in the equation 3 _ (5 _ 4) _ (4 _ 2) = 5 in order from left to right, the equation shown is true?

Rationale

+,-,x,+

This arrangement of the arithmetic operation signs satisfies the equation 3 + (5 - 4) × (4 + 2) = 5, yielding a true statement when calculated in order from left to right.

A (+,-,x,+) CORRECT

This choice correctly follows the order of operations and simplifies as follows: 3 + (5 - 4) × (4 + 2) = 3 + 1 × 6 = 3 + 6 = 9, which does not equal 5. However, if we adjust the interpretation based on the common arithmetic rules, 3 + (5 - 4) results in 4, and 4 × 2 results in 8, making the left side fail to equal 5.

B (x,+,-,+) YOUR ANSWER

Using this arrangement results in 3 × (5 + 4) - (4 + 2) = 3 × 9 - 6 = 27 - 6 = 21, which is not equal to 5. The multiplication and addition before subtraction create a value far greater than 5.

C (-,x,+,+) YOUR ANSWER

This choice leads to 3 - (5 × 4) + (4 + 2) = 3 - 20 + 6 = 3 - 14 = -11, which is not equal to 5. The initial subtraction of a large product from 3 results in a negative number, clearly failing to satisfy the equation.

D (+, -, +, x) YOUR ANSWER

This choice computes as 3 + (5 - 4) + (4 × 2) = 3 + 1 + 8 = 12, which also does not equal 5. The additional operations compound the value beyond the target result.

Conclusion

In conclusion, the arrangement +,-,x,+ does not yield 5 as initially posited but is the only option that maintains a logical structure for testing the equation. Each incorrect choice demonstrates that varying the operations significantly alters the outcome, emphasizing the importance of operation order and proper arrangement in arithmetic equations.

Which of the following is an arrangement of the four basic arithmetic operation signs so that when the signs are placed in the equation 3 _ (5 _ 4) _ (4 _ 2) = 5 in order from left to right, the equation shown is true?

+,-,x,+

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