Question

How do you solve $\dfrac{2}{3}x = 26$ ?

Answer 1

Hint: The given equation contains both numerical values and alphabets in one equation, so it is an algebraic expression, where x is the alphabet used that represents an unknown quantity. By solving the above equation, we mean to find the value of the unknown quantity. To find the value of n unknown quantities, we need n equations, so the value of x can be found easily as 1 equation is given to us. To solve this equation, we will rearrange the terms such that one side contains only terms of x variable and the other side contains only constant values.

Complete step-by-step solution:
We are given that $\dfrac{2}{3}x = 26$
We will take 3 and 2 to the right-hand side –
$
  x = \dfrac{3}{2} \times 26 \\
   \Rightarrow x = 3 \times 13 \\
   \Rightarrow x = 39 \\
 $
Hence, when $\dfrac{2}{3}x = 26$ , we get $x = 39$ .


Note: On taking the constant values on the right-hand side, we obtained a fraction $\dfrac{3}{2} \times 26$ . 26 and 3 are the numerator of this fraction, and 2 is present in the denominator. To find an accurate answer, we will simplify this fraction by prime factorization. Prime factorization is defined as the process of expressing a number as a product of its prime factors. Thus on expressing both the numerator and the denominator as a product of its prime factors, we will find out the factors that are present in both the numerator and the denominator and cancel out those factors. In the obtained fraction, 2 is common in both the numerator and the denominator, so on canceling them out we get a whole number as the answer.