Question

Fill in the boxes using the digits 1-9 at most once: _x + _ = _(x + _)

a) 2, 3, 5, 4
b) 3, 2, 4, 5
c) 1, 3, 2, 4
d) 4, 2, 5, 3

Answer 1

The Mathematics problem asks to fill in blanks with digits to create a valid equation. The correct answer is option c) 1×x + 3 = 2(x + 4) when x = 5, as it satisfies the constraints of using the digits 1-9 without repetition.

Step-by-step explanation:

The subject of this question is Mathematics. The problem involves filling in the blanks with digits 1-9 to create a valid equation, where each digit is used at most once. Out of the given options, let's consider each one:

• a) 2×x + 3 = 5(x + 4)
• b) 3×x + 2 = 4(x + 5)
• c) 1×x + 3 = 2(x + 4)
• d) 4×x + 2 = 5(x + 3)

We can quickly verify which of these options is correct by performing the multiplication and addition on the right side of each equation and seeing if it equals the left side.

1. For a), 2×x + 3 = 5x + 20, which is not true for any value of x.
2. For b), 3×x + 2 = 4x + 20, which could be true if x = 18, but that uses digits outside the 1-9 range and repeats the digit 8.
3. For c), 1×x + 3 = 2x + 8, which is true when x = 5. This uses the digits 1, 3, 2, 4, and 5 without repetition, so it satisfies the problem's constraints.
4. For d), 4×x + 2 = 5x + 15, which is not true for any value of x.

Therefore, the correct answer is c) 1×x + 3 = 2(x + 4) when x = 5.