Question

How do you solve \[9 - 2c + c = - 13\] ?

Answer 1

Hint: The algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. The given equation is a linear equation as there is a constant variable involved and to solve this equation, combine all the like terms and then simplify the terms to get the value of \[x\].

Complete step-by-step answer:
Let us write the given equation
\[\Rightarrow 9 - 2c + c = - 13\]
From the given equation, let us combine the like terms
\[\Rightarrow 9 - c = - 13\]
The obtained equation the terms are not arranged, hence rearrange the terms of the given equation
\[\Rightarrow 9 - c = - 13\]
\[ \Rightarrow \]\[ - c + 9 = - 13\]
Hence after rearranging both the sides of the equation, we get
\[\Rightarrow - c + 9 = - 13\]
Subtract 9 on both the sides of the obtained equation
\[ \Rightarrow - c + 9 - 9 = - 13 - 9\]
As we can see that -9 and +9 implies zero.
\[\Rightarrow - c = - 13 - 9\]
Subtracting the numbers in the equation, we get
\[\Rightarrow - c = - 22\]
To get the value of \[c\], divide both sides of the equation by the same term i.e., -1
\[\Rightarrow \dfrac{{ - c}}{{ - 1}} = \dfrac{{ - 22}}{{ - 1}}\]
\[\Rightarrow - c = \dfrac{{ - 22}}{{ - 1}}\]
Therefore, after simplifying the terms we get the value of \[c\] as:
\[\Rightarrow c = 22\]

Hence, the value of \[c\] in the given equation is \[c = 22\].

Additional information: 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.

Note: The key point to solve this type of equation is to combine all the like terms and evaluate for the variable asked. As we know that Simultaneous equations are two equations, each with the same two unknowns and are "simultaneous" because they are solved together and there are three methods to solve the system of linear equations in two variables are: Substitution method, Elimination method and Cross-multiplication method.