Question

How do you solve the linear equation \[7-3x=x-4\left( 2+x \right)\]?

Answer 1

Hint: In the above type of question we can easily see that the equation that has been mentioned is a type of linear equation which means that we will have to shift the variable on to either Right hand or towards the left hand side of the equation and then do the same with the constants, then solve the equation to find the final answer to the equation.

Complete step-by-step solution:
So in the above question the given function is as follows
\[7-3x=x-4\left( 2+x \right)\]to solve the above equation we will be first opening the bracket that is present on the right hand side of the equation from which we will get
\[\Rightarrow 7-3x=x-8-4x\]
After opening the bracket we will be able to see that there are two x terms one is negative and one is positive, now we are going to add them and make a final equation with left hand side and right hand side.
\[\Rightarrow 7-3x=-8-3x\]
Now we are going to make the shifting in which we are going to shift the x terms to one side of the equation can be the right hand side or can be the left hand side of the equation and then we are going to the same with the constants of the equation that are present. We are going to shift the constants to the other side of the equation i.e. if variables are in the left hand side then the constants will be on the right hand side and so with this we will get
\[\Rightarrow 3x-3x=7-8\]
Here we can see that in the final equation there is no x term left to find, so there is no solution to the whole equation.
So finally we can say that there is no solution to this equation.

Note: In this type of question that has been mentioned above there are some common mistakes that happen that we forget to apply the BODMAS rule, always apply the BODMAS rule so as to get the correct answer to the equation and when you are able to find the final answer always substitute it in the main equation so as to check whether what you have solved is correct or not.