Question

How do you combine like terms in \[\left( {5a - 9b - 2c} \right) + \left( {c - 7b - 3c} \right)\]?

Answer 1

Hint: The algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. In the given equation there are three constant variables involved and to solve this equation, as mentioned in the question we need combine all the like terms separately with respect to the variables and then simplify the terms together to obtain the simplified equation.

Complete step by step solution:
Let us write the given equation,
\[\left( {5a - 9b - 2c} \right) + \left( {c - 7b - 3c} \right)\]
In the given equation the terms are not arranged, hence combine and rearrange the terms of the given equation with respect to their variables.
So, combine the ‘a’ term, we get:
\[ = 5a\], as there is no other term.
Now, combine the b terms, we get:
\[ - 9b - 7b = - 16b\]
Next combine the c terms, as:
\[ - 2c + c - 3c = - 4c\]
Now, put your answers together, we get:
\[ = 5a - 16b - 4c\].
Therefore, after rearranging the equation, we get:
\[\left( {5a - 9b - 2c} \right) + \left( {c - 7b - 3c} \right) = 5a - 16b - 4c\].

Note: Equations that have more than one unknown can have an infinite number of solutions, finding the values of letters within two or more equations are called simultaneous equations because the equations are solved at the same time.
The key point to solve this equation is to combine all the like terms and evaluate for the variable asked. As, in this equation there are three different variables involved so we have solved it separately, as it seems easy to solve. And we know that Simultaneous equations are two equations, each with the same two unknowns and are "simultaneous" because they are solved together.