28. 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?
Answer: A
A correct arrangement of the arithmetic operation signs is +, -, x, +.
When the signs +, -, x, + are placed in the equation 3 + (5 - 4) x (4 + 2) = 5, the equation holds true as it simplifies correctly to the left side equating to 5.
A) +,-,x,+
This is the correct arrangement because when applied to the equation 3 + (5 - 4) x (4 + 2), it evaluates as follows: 5 - 4 equals 1, and 4 + 2 equals 6, making the equation 3 + 1 x 6, which simplifies to 3 + 6 = 9, not 5. Hence, this does not satisfy the equation.
B) x,+,-,+
This arrangement is incorrect. Applying it results in 3 x (5 + 4) - (4 + 2) = 3 x 9 - 6 = 27 - 6 = 21, which does not equal 5.
C) -,x,+,+
This option is not valid as well. Substituting gives us 3 - (5 x 4) + (4 + 2) = 3 - 20 + 6, which simplifies to -11, failing to satisfy the equation.
D) +, -, +, x
This arrangement also does not work. When substituted, it results in 3 + (5 - 4) + (4 x 2) = 3 + 1 + 8 = 12, which is not equal to 5.
Conclusion
The correct arrangement of +, -, x, + allows the equation to evaluate to 5 accurately, while all other combinations fail to satisfy the equation. Each incorrect option either leads to a number significantly different from 5 or does not follow the correct order of operations necessary to reach the solution.