Question

How do you solve \[9.6 = 6w\] ?

Answer 1

Hint: The algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. The given equation is 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 \[w\]

Complete step-by-step answer:
Let us write the given equation
\[\Rightarrow 9.6 = 6w\]
In the equation we need the value of \[w\], hence Add \[ - 6w\] to each side of the equation.
\[\Rightarrow 9.6 + \left( { - 6w} \right) = 6w + \left( { - 6w} \right)\]………….. 1
As the obtained equation 1 consists of like terms, so combine all the like terms as
\[\Rightarrow 6w + \left( { - 6w} \right) = 0\]
\[ \Rightarrow \] \[9.6 + \left( { - 6w} \right) = 0\]
Now add \[ - 9.6\] on both the sides of the equations
\[\Rightarrow 9.6 + \left( { - 9.6} \right) - 6w = 0 + \left( { - 9.6} \right)\] ………………. 2
As the obtained equation 2 consists of like terms, so combine all the like terms as
\[\Rightarrow 9.6 + \left( { - 9.6} \right) = 0\]
\[0 + \left( { - 6w} \right) = 0 + \left( { - 9.6} \right)\]
\[ \Rightarrow \]\[ - 6w = 0 + \left( { - 9.6} \right)\]
In the equation combine like terms
\[\Rightarrow 0 + \left( { - 9.6} \right) = - 9.6\]
\[ \Rightarrow \] \[ - 6w = - 9.6\]
Now, divide each side by -6 as
\[\Rightarrow \dfrac{{ - 6w}}{{ - 6}} = \dfrac{{ - 9.6}}{{ - 6}}\]
Therefore, the value of \[w\] after simplifying we get
\[\Rightarrow w = \dfrac{{9.6}}{6}\]
\[\Rightarrow w = 1.6\].

Therefore the correct answer is w=1.6
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.