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Problem 2

# Show that $$(-2)+(-3)=-5$$.

Expert verified
To show that $$(-2) + (-3) = -5$$, we first add the absolute values of the numbers, which are 2 and 3, resulting in 5. Since both original numbers are negative, we apply the negative sign back to the result, giving us -5. Thus, $$(-2) + (-3) = -5$$.
See the step by step solution

## Step 1: Understand integer addition properties

When adding integers, we must take into account the signs of the numbers we are dealing with. In this case, both numbers are negative. The sum of two negative numbers will also result in a negative number with a higher absolute value.

## Step 2: Add the absolute values of the numbers

Since both numbers are negative, we can simply ignore the negative signs for now and add the absolute values together. In this case, the absolute values are 2 and 3. Adding these together, we get 2 + 3 = 5.

## Step 3: Apply the negative sign back to the result

We previously ignored the negative signs of the numbers in order to add their absolute values. However, we need to apply the negative sign back to our result. Since the sum of the absolute values was 5, the sum of the original numbers (-2 and -3) is -5.

## Step 4: Verify the result

We have shown that $$(-2) + (-3) = -5$$ by adding the absolute values of the numbers and applying the negative sign back to the result. This result can now be verified as correct, demonstrating that $$(-2) + (-3) = -5$$.

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