Evaluate \[\left( { - 10} \right) + \left( { + 19} \right)\].

Hint: Here we have a simple algebraic expression, we need to simplify it by applying the given operations. That is addition, subtraction, division and multiplication. We need to expand the brackets then we subtract one with the other.

Complete step by step solution:
Given,
\[\left( { - 10} \right) + \left( { + 19} \right)\]
The meaning of this question is
\[1 \times \left( { - 10} \right) + 1 \times \left( { + 19} \right)\]
\[ - 10 + 19\]
Now subtracting we have,
\[ \Rightarrow 9\].
Thus, the value of \[\left( { - 10} \right) + \left( { + 19} \right) = 9\].

Note:
To solve the algebraic equation we use the BODMAS rule. This rule states that when given an equation or expression, we should first calculate the brackets, then any order, then division, then multiplication, then addition and then subtraction. Sometimes BODMAS is also called BIDMAS. Where ‘I’ is index and rest is the same. If we do the calculation with applying this rule we will get a wrong answer.
We know that the product of two negative numbers results in a positive number. The product of a positive (negative) number and a negative (positive) number results in a negative number only.