Question

How do you solve $3x = 27$?

Answer 1

Hint: In order to determine the value of x from the above question, transpose 3 from LHS to the denominator of RHS and write the numerator and denominator in the form of their factors and try to cancel out factors from numerator and denominator, you’ll get your required result.

Complete step by step solution:
Given a expression $3x = 27$
Transposing 3 from LHS to the denominator of RHS
$x = \dfrac{{27}}{3}$
To Convert this into its simplest form, factorise the numerator as well as denominator .
Since denominator is prime number so there is no factor, but numerator can be written as $3 \times 7$
Rewriting the fraction into their factors form as
\[ \Rightarrow x = \dfrac{{3 \times 7}}{{3 \times 1}}\]
Cancelling out $3$ as it is coming in numerator and denominator.
\[
   \Rightarrow x = \dfrac{{{3} \times 7}}{{{3} \times 1}} \\
   \Rightarrow x = \dfrac{7}{1} \\
   \Rightarrow x = 7 \\
 \]
Therefore, the value of x in the expression $3x = 27$ is equal to 7.

Note: 1.What is a Rational Number?
A Rational number is a number which can be expressed in the form of $\dfrac{p}{q}$, where p and q are any integer value and q is not equal to 0. Such a number is known as a rational number.
2.What is a Linear Equation?
A linear equation is an equation which is in the form of $ax + b$, where a,b are numbers and $a \ne 0$. The degree of the linear equation is of order 1. Solution of any linear equation leads to a single value of x.