Question

How do you solve $\dfrac{7}{5} = \dfrac{x}{3}$?

Answer 1

Hint: First we have to find the least common multiple (LCM) of all the denominators in the given equation. Next, we have to multiply both sides of the equation with the LCM of denominators. Next step is to isolate the variable terms on one side, and the constant terms on the other side. Next step is to make the coefficient of the variable equal to $1$ using multiplication or division property.

Complete step-by-step solution:
The algebraic equation is $\dfrac{7}{5} = \dfrac{x}{3}$.
We have to find the value of $x$.
First we have to find the least common multiple (LCM) of all the denominators in the given equation.
Denominator of $\dfrac{7}{5}$ is $5$ and the denominator of $\dfrac{x}{3}$ is $3$.
So, we have to find the LCM of $5$ and $3$.
Since, both $5$ and $3$ are prime numbers. So, their LCM will be $15$.
LCM of $5$ and $3$ $ = 15$
Now, we have to multiply both sides of the equation with the LCM of $5$ and $3$.
So, multiplying both sides of equation $\dfrac{7}{5} = \dfrac{x}{3}$ by $15$.
$21 = 5x$
Next step is to isolate the variable terms on one side, and the constant terms on the other side.
Here, variable terms and constant terms are already on different sides.
Next step is to make the coefficient of the variable equal to $1$.
So, dividing both sides of the equation by $5$.
$\therefore x = \dfrac{{21}}{5}$
Therefore, $x = \dfrac{{21}}{5}$ is the solution of $\dfrac{7}{5} = \dfrac{x}{3}$.

Note: An algebraic equation is an equation involving variables. It has an equality sign. The expression on the left of the equality sign is the Left Hand Side (LHS). The expression on the right of the equality sign is the Right Hand Side (RHS).
In an equation the values of the expressions on the LHS and RHS are equal. This happens to be true only for certain values of the variable. These values are the solutions of the equation.