Question

How do you solve: $6\left( {10 - x} \right) = 90$ ?

Answer 1

Hint: The value of x in $6\left( {10 - x} \right) = 90$ can be found by using the method of transposition. Method of transposition involves doing the exact same mathematical thing on both sides of an equation with the aim of simplification in mind. This method can be used to solve various algebraic equations like the one given in question with ease.

Complete step by step answer:
We would use the method of transposition to find the value of x in $6\left( {10 - x} \right) = 90$.
Method of transposition involves doing the exact same thing on both sides of an equation with the aim of bringing like terms together and isolating the variable or the unknown term in order to simplify the equation and finding the value of the required parameter.
Now, In order to find the value of x, we need to isolate x from the rest of the parameters.
So, we have, $6\left( {10 - x} \right) = 90$
Opening the brackets, we get,
$ \Rightarrow 60 - 6x = 90$
Taking all the terms consisting x to the right side of the equation and constant terms to the left side of equation, we get,
$ \Rightarrow 60 - 90 = 6x$
We must remember to reverse the signs of the terms while shifting the terms from one side of the equation to the other side.
Now, adding up the like terms, we get,
$ \Rightarrow - 30 = 6x$
Changing the sides of equation, we get,
$ \Rightarrow 6x = - 30$
Dividing both the sides of the equation by $6$, we get,
$ \Rightarrow x = - \dfrac{{30}}{6}$
Cancelling the common factors in numerator and denominator, we get,
\[ \Rightarrow x = - \dfrac{{6 \times 5}}{6}\]
\[ \Rightarrow x = - 5\]
Hence, the value of x in $6\left( {10 - x} \right) = 90$ is $ - 5$.

Note:
If we add, subtract, multiply or divide by the same number on both sides of a given algebraic equation, then both sides will remain equal.
We can solve linear equations in one variable by various methods:
1. Trial and error
2. Inverse operation