Question

How do you solve \[ - 9 + 8k = 7 + 4k\] ?

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 k.

Complete step-by-step answer:
Let us write the given equation
\[\Rightarrow - 9 + 8k = 7 + 4k\]
In the given equation the terms are not arranged, hence rearrange the terms of the given equation
\[ - 9 + 8k = 7 + 4k\]
\[ \Rightarrow \]\[8k - 9 = 7 + 4k\]
Hence after rearranging both the sides of the equation, we get
\[\Rightarrow 8k - 9 = 4k + 7\]
Add 9 on both the sides of the obtained equation
\[\Rightarrow 8k - 9 + 9 = 4k + 7 + 9\]
As we can see that -9 and +9 implies zero.
Adding the numbers in the equation, we get
\[\Rightarrow 8k = 4k + 16\]
Now let us subtract \[4k\] from both sides of the equation as
\[\Rightarrow 8k - 4k = 4k + 16 - 4k\]
As the equation consists of like terms, so let us combine all the like terms and simplify it
\[\Rightarrow 4k = 4k + 16 - 4k\]
\[ \Rightarrow \]\[4k = 16\]
Therefore, we get the value of k as
\[\Rightarrow k = \dfrac{{16}}{4}\]
\[\Rightarrow k = 4\]

Hence, the value of k in the given equation is \[k = 4\].

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.