Question

How do you solve \[\dfrac{2}{3}x - 5 = 1\] ?

Answer 1

Hint: The mathematical equations containing a combination of numerical values and alphabets are called algebraic expressions. The alphabets in the algebraic expression represent some unknown variable quantity. Thus, the equation given in the equation is an algebraic equation. $ \dfrac{2}{3} $ is a fraction that is in multiplication with x, and is then subtracted with 5, this equation is equal to 1. So we can solve the given equation by taking the constant terms at one side and unknown quantity x on the other side and then we apply the given arithmetic operations

Complete step-by-step answer:
We have to solve $ \dfrac{2}{3}x - 5 = 1 $
Rearranging the given equation, we get –
 $
  \dfrac{2}{3}x = 1 + 5 \\
   \Rightarrow \dfrac{2}{3}x = 6 \\
   \Rightarrow x = 6 \times \dfrac{3}{2} = \dfrac{{18}}{2} \;
  $
Now, we see that the obtained value of x is a fraction, so we have to convert it in the most simplified form as follows –
 $
  x = \dfrac{{18}}{2} = \dfrac{{2 \times 3 \times 3}}{2} = 3 \times 3 \\
   \Rightarrow x = 9 \;
  $
Hence, when $ \dfrac{2}{3}x - 5 = 1 $ , we get $ x = 9 $
So, the correct answer is “ $ x = 9 $ ”.

Note: In simple words, algebra is known as the representation of numbers by alphabets in a formula or equation involving mathematical operations. We require n number of equations for finding the values of n unknown variables, here we have to find the value of only one unknown quantity so one equation is enough to find the value of x. At last we have obtained the answer in terms of a fraction. To simplify the fraction, we write the numerator as a product of its prime factors and then we cancel out the factors that are in common in the numerator and the denominator. We can solve similar questions using the above-mentioned method.