Question

How do you solve for $x$ in $x = 2.54x$ ?

Answer 1

Hint: In this question, we are given an algebraic expression containing one unknown variable quantity. We know that to find the value of “n” unknown variables, we need “n” number of equations. In the given algebraic expression, we have 1 unknown quantity and exactly one equation to find the value of x. For that, we will rearrange the equation such that x lies on the one side of the equation and all other terms lie on the other side. Then by applying the given arithmetic operations, we can find the value of x.

Complete step-by-step solution:
We are given that $x = 2.54x$
To find the value of x, we will take $2.54x$ to the left-hand side –
$ \Rightarrow x - 2.54x = 0$
Taking x common, we get –
$
  \Rightarrow x(1 - 2.54) = 0 \\
   \Rightarrow x( - 1.54) = 0 \\
 $
To find the value of x, we will take -1.54 to the right-hand side –
$
 \Rightarrow x = \dfrac{0}{{ - 1.54}} \\
   \Rightarrow x = 0 \\
 $
Hence, when $x = 2.54x$ , we get $x = 0$

Note:The mathematical equations that are a combination of numerical values and alphabets are known as algebraic expressions. The alphabets represent some unknown quantities, the alphabets and numerical values are linked via arithmetic operations like addition, subtraction, multiplication and division. Note that the equation is of the form $x = nx$ , we know that all the numbers are equal to each other, but cannot be equal to some number multiplied with itself. For example, $2 = 2$ but $2 \ne 2(2)$ . The only number that remains unchanged on getting multiplied by any number is zero. Hence, we can also find the answer to this question theoretically as mentioned above.