Question

What is the value of ‘x’ in the equation \[5{x^3} = 135\]?

Answer 1

Hint: Here we need to solve for ‘x’. Since we have a small number on the right hand side of the equation we can solve this using trial and error method by giving values for x or we can solve this using the transposition method and on further simplification we will have the desired result.

Complete step by step solution:
Given \[5{x^3} = 135\]
Now by using the transposition method we transport 5 to the right hand side of the equation by dividing 5 on the right hand side.
\[{x^3} = \dfrac{{135}}{5}\]
\[{x^3} = 27\]
Taking cube root on both side we have,
\[x = \sqrt[3]{{27}}\]
We know that 27 is a perfect cube then we have,
\[x = \sqrt[3]{{{3^3}}}\]
\[ \Rightarrow x = 3\]. This is the required result.
So, the correct answer is “x = 3”.

Note: We can check whether the obtained answer is correct or not by substituting x value in the given problem,
\[5{x^3} = 135\]
\[5{\left( 3 \right)^3} = 135\]
\[5\left( {27} \right) = 135\]
\[ \Rightarrow 135 = 135\]. Hence the obtained answer is correct. We also know that the cube of any negative number will yield a negative number, while the square of any negative number yields a positive number only.