Question

What is \[3\omega +6=4\omega \]?

Answer 1

Hint: Given equation \[3\omega +6=4\omega \] is a linear equation with a single variable \[\omega \].now we have to solve for \[\omega \] because \[\omega \] is the root of the given equation \[3\omega +6=4\omega \]. We should avoid calculation mistakes to get accurate answers while solving these kinds of questions.

Complete step by step solution:
From the question we were given the equation as \[3\omega +6=4\omega \].
\[3\omega +6=4\omega \] is a linear equation with a single variable \[\omega \]
S0, clearly, we know \[\omega \] is the root of the given equation.
From the question it is clear that we have to find the value of \[\omega \].
So, lets us try to find the value of \[\omega \].
\[3\omega +6=4\omega \] is the given equation from the question.
Now let us try to move all the terms containing \[\omega \]to one side of the equation.
So, now subtract \[4\omega \] from both sides. we get,
\[\Rightarrow \]\[3\omega +6-4\omega =4\omega -4\omega \];
Now subtract \[4\omega \] from \[3\omega \]. We will get\[-\omega \]
Now equation can be written as
\[\Rightarrow \]\[-\omega +6=0\]
Now, let us subtract \[6\]on both sides of the equation,
Now we will get equation as
\[\Rightarrow \]\[-\omega +6-6=0-6\]
On simplification we will get
\[-\omega =-6\]
Now let us multiply with \[-1\]on both sides, we get
\[\Rightarrow \]\[-\omega \times \left( -1 \right)=-6\times \left( -1 \right)\]
Multiplication of \[-\omega \] with \[-1\] we get \[\omega \]
Now we get the equation as,
\[\omega =6\]
So, we got \[\omega =6\] which is the root of the given linear equation \[3\omega +6=4\omega \].
Now, we can conclude that \[\omega =6\] is the root of the given linear equation \[3\omega +6=4\omega \].

Note: students should use proper transformations such as additions, subtractions, multiplication, divisions whenever needed. we should be careful while doing calculations otherwise it will lead to major errors in the final answer while finding the root of the given equation \[3\omega +6=4\omega \].