Question

What is the value of $x$ in the equation $\dfrac{x-2}{3}+\dfrac{1}{6}=\dfrac{5}{6}?$

Answer 1

Hint: We solve this question for x by rearranging and simplifying the given algebraic expression. We take all the constant terms to one side and simplify. Then we cross multiply the denominators and solve for x.

Complete step by step solution:
In order to solve this question, let us consider the given algebraic expression.
$\Rightarrow \dfrac{x-2}{3}+\dfrac{1}{6}=\dfrac{5}{6}$
We take all the constant terms to one side. Therefore, we subtract both sides of the equation by the term $\dfrac{1}{6},$
$\Rightarrow \dfrac{x-2}{3}+\dfrac{1}{6}-\dfrac{1}{6}=\dfrac{5}{6}-\dfrac{1}{6}$
We cancel the two $\dfrac{1}{6}$ terms on the left-hand side of the equation. Now since the denominators of both the terms on the right-hand side of the equation is the same, we subtract their numerators directly as shown.
$\Rightarrow \dfrac{x-2}{3}=\dfrac{5-1}{6}$
Subtracting the numerators on the right-hand side,
$\Rightarrow \dfrac{x-2}{3}=\dfrac{4}{6}$
Cross multiplying both sides of the equation,
$\Rightarrow 6\left( x-2 \right)=4\times 3$
Multiplying the term in the brackets with 6 on the left-hand side and multiplying the two terms on the right-hand side,
$\Rightarrow 6x-12=12$
Adding both sides of the equation with 12,
$\Rightarrow 6x=12+12$
Adding the terms on the right-hand side,
$\Rightarrow 6x=24$
Dividing both sides of the equation by 6,
$\Rightarrow x=\dfrac{24}{6}$
Dividing both the terms on the right-hand side of the equation,
$\Rightarrow x=4$

Hence, the value of $x$ in the equation $\dfrac{x-2}{3}+\dfrac{1}{6}=\dfrac{5}{6}$ is 4.

Note:
We need to know the basic ways to solve an algebraic equation in order to solve this question. We need to be careful while dealing with fractions because students tend to make mistakes in these types of questions. We can also solve this question by first taking the LCM for the two terms on the left-hand side and then cancelling the same denominators on both sides of the equation. This will give us the same result.