Question

How do you solve $ \dfrac{4}{6} = \dfrac{8}{{x - 1}}? $

Answer 1

Hint: Take the given expression and perform cross multiplication in the equation and then simplify the equation using the basic mathematical concepts and find the resultant required value for “x”.

Complete step by step solution:
Take the given expression: $ \dfrac{4}{6} = \dfrac{8}{{x - 1}} $
In the cross multiplication, the numerator of one side is multiplied with the denominator of the opposite and similarly the denominator of one side is multiplied with the numerator of the opposite side.
 $ 4(x - 1) = 8(6) $
Simplify the above equation finding the product of the terms on both the sides of the equation.
 $ 4x - 4 = 48 $
Move constant from the left hand side of the equation to the right hand side of the equation. When you move any term from one side to the another then the sign of the term also changes. Negative term becomes positive and the positive term becomes negative term.
 $ 4x = 48 + 4 $
Simplify the above equation finding the addition of the terms on the right hand side of the equation.
 $ 4x = 52 $
Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
 $ x = \dfrac{{52}}{4} $
Find the factors in the term for the numerator.
 $ x = \dfrac{{4 \times 13}}{4} $
Common factors from the numerator and the denominator cancels each other. Therefore, remove from the numerator and the denominator from the above expression.
 $ x = 13 $
This is the required solution.
So, the correct answer is “ $ x = 13 $ ”.

Note: Be careful about the sign convention and about the very first step while simplification. Do it wisely and then simplify using the basic mathematical rules. Be good in multiples and division. Since it is the most important fundamental to solve and simplify any mathematical expression. Remember multiples till twenty numbers. Always try to convert the given number in the prime numbers and then find the common factors in the numerator and the denominator and then remove them.