Each integer from -3 to 5 inclusive is placed in the diagram, with one number going into each box. If the sum of the numbers in each row is the same, what is that sum? (the diagram will be a screenshot) A. 0 b. 3 c. 5 d.6

Our solution is option b, or in other words 3.

Step-by-step explanation:

This is more of a " guess and try " question. Say that 3 is the solution. If that is so, let us prove it, by arranging the values such that their addition is equivalent to 3 in each row.

Take - 3 as the first value in the first row. What other combinations can go with this, but still meet our requirement of a total of 3? The other two numbers must have a sum of 6, so let's list all possibilities -

{ 5 and 1 }

{ 4 and 2 }

Let us try 5 and 1. We should receive the following table so far -

| - 3 | 5 | 1 |

|   ?  | ? | ? |

|   ?  | ? | ? | Now for this second row let - 2 be the starting value. The only possible values in the row should have a sum of 5 to have a total of 3 -

{ 3 and 2 }

This is the only possibility we have here. Plug it into our table,

| - 3 | 5 | 1 |

| - 2 | 3 | 2 |

|   ?  | ? | ? | Let's begin with the value - 1 for the third row. The only remaining values that could fill this row are 0 and 4. { - 1, 0, and 4 } add to 3, and hence the sum of the number in each row is a constant, 3. It has been proved.

| - 3 | 5 | 1 |

| - 2 | 3 | 2 | - This is our table.

| - 1  | 0 | 4 |

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^