Question

Solve:
\[\dfrac{x}{5}=\dfrac{x-1}{6}\]

Answer 1

Hint: We are given an algebraic expression with ‘x’ as variable and we are asked to solve the given expression and find the value of ‘x’. We will first cross multiply the denominators across the equality sign to the opposite numerators. Then, we will write the expression in terms of ‘x’ and find the respective value of ‘x’. Hence, we will have the required value.

Complete step by step answer:
According to the given question, we are given an algebraic expression in terms of ‘x’ and we are asked to find the value of ‘x’.
The expression that we have is,
\[\dfrac{x}{5}=\dfrac{x-1}{6}\]
We will first simplify the given expression and write it in terms of ‘x’ and then we will have the value of ‘x’. We have,
We will cross multiply the denominators across the equality to the opposite numerators and we get,
\[\Rightarrow 6x=5\left( x-1 \right)\]
Opening up the brackets, we will multiply 5 to both ‘x’ and -1 and we will 5x and -5 respectively and we get the expression as,
\[\Rightarrow 6x=5x-5\]
We will write the expression in terms of ‘x’, we get,
\[\Rightarrow 6x-5x=-5\]
We have the value of ‘x’ as,
\[\Rightarrow x=-5\]
Therefore, the value of \[x=-5\].

Note: The simplification of the expression should be done carefully. Also, the cross multiplication of the terms across the equality sign should not get interchanged and is instead multiplied to the same fraction. This should not happen else the solution will get wrong. We can check if the answer obtained is correct or not, by substituting the value of ‘x’ back in the expression and if LHS = RHS, then the value obtained is correct.