Question

How do you solve and check your solution to \[\dfrac{1}{3}c = 32\]?

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 is a constant variable involved and to solve this equation, we just need to shift the terms and combine the terms and then simplify the terms to get the value of c, next substitute the value of c to show LHS = RHS i.e., \[\dfrac{1}{3}c = 32\].

Complete step by step solution:
Given,
\[\dfrac{1}{3}c = 32\],
The given equation is written as:
\[ \Rightarrow \dfrac{c}{3} = 32\]
Shift the terms, to get the value of c as:
\[ \Rightarrow c = 32 \times 3\]
\[ \Rightarrow c = 96\]
Hence, now substitute the value c in the given equation to show LHS = RHS as:
\[ \Rightarrow \dfrac{c}{3} = \dfrac{{96}}{3}\]
Hence, we get:
\[ \Rightarrow c = 96\]

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.
Solving simultaneous equations by Substitution: The substitution method is the algebraic method to solve simultaneous linear equations. In this method, the value of one variable from one equation is substituted in the other equation. In this way, a pair of the linear equations gets transformed into one linear equation with only one variable, which can then easily be solved.

Note: The key point to solve this type of equations is to combine and shift the terms, to evaluate for the variable asked and we must also know that if there are two variables involved in the equation then, it is called as Simultaneous equations are two equations, each with the same two unknowns and are simultaneous because they are solved together.