SOLUTION: Why are + signs sometimes left out of problems. When I do -3(2t+6) I get -6t+(-18). But my book and calculators both say -3(2t+6)=-6t-18. What happened to the + between the

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Question 1011285: Why are + signs sometimes left out of problems. When I do -3(2t+6) I get -6t+(-18). But my book and calculators both say -3(2t+6)=-6t-18. What happened to the + between the t and the 6?
Found 2 solutions by josgarithmetic, Edwin McCravy:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
Why? If A NUMBER has no sign on or in front of it, the sign IS ASSUMED to be PLUS for POSITIVE; Not that the number is positive, but that the SIGN is positive. If a negative sign is intended, then this negative sign is NEEDED; otherwise the PLUS sign is assumed.

You first learn about numbers when you learn to count and learn to add and subtract. At that stage, you would not understand positive and negative numbers. All numbers have no sense with signs of PLUS OR MINUS; you only are learning about Whole Numbers, and the four basic arithmetic operations.

A few years later, you learn about extending a number line to BOTH sides of zero; so you have numbers increasing toward the right which become the POSITIVE numbers, and you have numbers decreasing toward the left which become the NEGATIVE numbers. You also are taught how to understand and perform both addition and subtraction USING the number line and during this learning is when you develop your understanding and skill to sort through Additions and Subtractions of signed numbers.

The way to make some progress with this is to study Introductory or Elementary Algebra.
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
Because 

"plus a negative number" 

always means the same as 

"minus the corresponding positive number, 

and it is shorter to write

A-B 

than to write

A+(-B)

What you should learn to do is to pretend that
a minus sign IS a negative sign!  Pretend that it is
the sign of the number that follows it.  After all,
a negative sign and a minus sign look exactly alike. 
So when you see

A-B

learn to think of the - before the B as if it were actually 
the negative sign of B, (even though it really isn't.)
But think of it that way anyway.  When the sign is 
between the A and the B you know that it is A plus 
-B.

Edwin
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