# How To Solve Integer Problems

What happens when we add integers with unlike signs?How do we add a positive and a negative integer, or a negative and a positive integer? Subtract the smaller number from the larger number you get in Step 1. The result from Step 2 takes the sign of the integer with the greater absolute value. The example of non-consecutive odd integers, if someone went from 3 straight to 7, these are not consecutive. Well as you can imagine, a little bit of algebra might be handy here.

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Well if you add 2 again, if you add 2 to x plus 2, well now you get to x plus 4.

So our four consecutive odd integers are 31, 33, 35, and 37.

Summary: Adding two positive integers always yields a positive sum; adding two negative integers always yields a negative sum.

To find the sum of a positive and a negative integer, take the absolute value of each integer and then subtract these values.

Answer: -2.) When multiplying integers, we can think of multiplying "blocks" of negative numbers.

(a) Here is an integer times an integer: Notice that we were multiplying a positive number by a negative number and our result was negative.Refer to the following related topics for other types of integer word problems.Initially, there were the same number of blue marbles and red marbles in a bag. The following videos give more examples of integer word problems. So with that out of the way, let's actually try to tackle this question. So if you added 1, you'd just get to an even number, so you have to add 2 to get to the next odd one. So if x is the smallest of the four consecutive odd integers, how can we express the other three in terms of x? Well to get rid of that 12, we'd want to subtract 12 from the left-hand side. So let's let x be equal to the smallest of the four. So we have one x, two x's, three x's, four x's. And then we have 2 plus 4, which is 6, plus another 6 is 12. So to solve for x, a good starting point would be to just to isolate the x terms on one side of the equation or try to get rid of this 12. And if you don't feel like doing that in your head, you could also, of course, do traditional long division. Notice that opposite is not the same as absolute value. (a) ` -2 5` means "start at `-2` and go `5` in the positive direction" So we have: It is -4° and snowing. (a) ` -4 - (-3) = -4 ( 3) = -1 ` (We added 3 because the opposite of -3 is 3.) (b) `5 - ( 7) = 5 (-7) = -2.` (We added -7 because the opposite of 7 is -7.The forecast for tomorrow is for a rise in temperature of 6°. Eventually you’ll see the question is the same as "5 - 7" and we can do this as a journey: Start at 5 and move 7 units to the left.One of the biggest problems people have in mathematics is with negative numbers. A negative number is any number whose value is less than zero. In each example, the number on the right is the distance from 0.The opposite of an integer is obtained by changing its sign. (a) The opposite of `-3` is `3` and (b) The opposite of `4` is ` -4`. We can change the subtraction into a more familiar addition by realising that subtracting an integer is the same as adding its opposite.