Question

How do you solve \[\dfrac{m}{{10}} = \dfrac{{10}}{3}\]?

Answer 1

Hint: For solving the given equation, we need to separate the variable \[m\] on the left-hand side and all the constants on the right-hand side. For this, we have to multiply both sides of the given equation by \[10\] so that the denominator on the left-hand side of the given equation gets canceled and we are left with only the variable \[m\] in the left-hand side. Then, we will simplify the equation further to get the required value.

Complete step-by-step solution:
The equation which is given in the question is written as
\[\dfrac{m}{{10}} = \dfrac{{10}}{3}\]
Solving this equation means obtaining the value of the variable \[m\] from the given equation. We can see the highest power of the variable \[m\] in the given equation is equal to one. This means that the equation is linear and therefore it will have only one solution.
For solving the above equation, we multiply both the sides by \[10\] and get
\[ \Rightarrow \dfrac{m}{{10}} \times 10 = \dfrac{{10}}{3} \times 10\]
Cancelling \[10\] on the LHS, we get
\[\begin{array}{l} \Rightarrow m = \dfrac{{10}}{3} \times 10\\ \Rightarrow m = \dfrac{{100}}{3}\end{array}\]
Dividing 100 by 3, we get
\[ \Rightarrow m = 33\dfrac{1}{3}\]

Hence, the solution of the given equation is \[m = 33\dfrac{1}{3}\].

Note:
The given equation is a linear solution and thus we got only one solution. A linear equation is defined as an equation that has the highest degree of variable as 1 and has only one solution. The solution of an equation depends on the highest degree of the equation. For example, a quadratic equation has the highest degree of 2 and has 2 solutions. Similarly, a cubic equation has the highest degree of 3 and has 3 solutions.