Question

How do you solve $\dfrac{x}{2} + \dfrac{x}{4} = 5$?

Answer 1

Hint: To solve such questions first make the denominators of the LHS same. The least common denominator can be used to remove the fraction if there are any fractions in the given equation. After that simplify the LHS. Finally, equate the LHS to the RHS to get the value of $x$.

Complete step-by-step solution:
Given the equation $\dfrac{x}{2} + \dfrac{x}{4} = 5$.
To solve this equation we have to find the value of $x$.
Consider the LHS. That is,
$\dfrac{x}{2} + \dfrac{x}{4}$
First, make the denominator the same. That is,
$\dfrac{{x \times 2}}{{2 \times 2}} + \dfrac{x}{4} = \dfrac{{2x}}{4} + \dfrac{x}{4}$
Next, simplify the above equation. That is,
$\dfrac{{2x}}{4} + \dfrac{x}{4} = \dfrac{{3x}}{4}$
So, LHS becomes $\dfrac{{3x}}{4}$.
Equate the LHS to the RHS. That is,
$\dfrac{{3x}}{4} = 5$
Taking the denominator of LHS to the RHS, we get
$3x = 5 \times 4$
$3x = 20$
Divide both sides of the equation with the number $3$. That is,
$x = \dfrac{{20}}{3}$

Therefore, the solution to the given equation $\dfrac{x}{2} + \dfrac{x}{4} = 5$ is $x = \dfrac{{20}}{3}$.

Note: Variables can be defined as a quantity that is not fixed. An algebraic expression can be made up of variables, constants, and operators. An equation can be defined as one which allows only a specific value of a variable. For a given term to be an equation, the left-hand side should be equal to the right-hand side. If they are not equal then it cannot be an equation. The value of the variable, which we get by solving the equation, is known as the solution of the equation.
While solving such questions always remember to start solving the left-hand side of the equation. Then equate the left-hand side to the right-hand side to find the solution. Also one can verify whether the obtained value of $x$ is correct or not by substituting it in the LHS of the equation.