The equation is y = 3x - 24.
The number machine shows that first an operation is performed on x, and then the result is multiplied by 3.
This means the machine represents the equation y = 3(x + ?).
We can expand this to y = 3x + 3?.
Comparing this to the given equation y = 3x - 24, we can see that 3? must be equal to -24.
To find the value in the box, we solve for ?:
3? = -24
? = -24 ÷ 3
? = -8.
So the operation in the first box is "- 8".
Full Answer
The first box should be "- 8".
The number machine shows that the input `x` first goes through an unknown operation, and then the result of that is multiplied by 3 to get the output `y`.
Let the unknown operation be represented by a box, so the intermediate value is (x [box]).
The final output is y = 3 × (x [box]).
We are given that the overall equation is y = 3x - 24.
We can factorise the right-hand side of this equation by taking out a common factor of 3:
y = 3(x - 8).
Now we can compare this with the structure from the number machine:
y = 3(x - 8)
y = 3 × (x [box])
By comparing these, we can see that the expression in the brackets must be the same.
(x - 8) = (x [box])
Therefore, the operation in the box must be **- 8**.
Common mistakes
✗ Putting "-24" in the first box. This would give y = 3(x-24) = 3x - 72, which is incorrect.\n✗ Trying to work backwards and dividing by 3 first, which is not the order shown.
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