Add without using the number line
\[( - 10) + ( + 19)\]

Hint: Remove the brackets and then gain a proper sum and if eventually it comes out to be subtraction then write it accordingly to have less confusion. Also use the BODMAS rule while solving this question.

Complete step-by-step answer:
We will use the BODMAS rule to solve this question where we know that BODMAS stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. The BODMAS is used to explain the order of operation of a mathematical expression.
Clearly here in BODMAS, B stands for Bracket, O stands for OF, D stands for Division,M stands for multiplication, A stands for Addition and S stands for subtraction which is indeed the last among all.
We are given that \[( - 10) + ( + 19)\] and if we try to remove brackets we are left with
\[ - 10 + 19\] because \[( + ) \times ( + ) = ( + )\] no as we can see that 10 is less than 19
Then it will be of worth to write it as \[19 - 10\]
\[\begin{array}{*{20}{c}}
{}&{}&{}&{19}\\
{}&{}& - &{10}\\
{}&{}&{}&{\_\_\_\_}\\
{}&{}&{}&{09}
\end{array}\]
Hence 9 is the correct answer.

Note: One may not write it as \[19 - 10\] and directly do it in \[ - 10 + 19\] form because we know that \[( - ) + ( + ) = ( - )\] so it was clear that we will have to subtract and in the answer whoever of them is greater the sign they posses is copied here in this case 19 was greater than 10 and its sign was (+). In some regions, the BODMAS is also known as PEMDAS which stands for Parentheses, Exponents, Division, Multiplication, Addition, and Subtraction.