Question

How do you solve \[5x + 10x = 90\] ?

Answer 1

Hint: In the given question, we have been asked to solve a linear equation with a single variable. Since in the equation variable has power of 1, $ x $ will have unique value. In order to proceed with the following question we need to rearrange operations like terms i.e .all the variables together and constants together.

Complete step-by-step answer:
We are given,
 \[5x + 10x = 90\]
As we understand that two numbers can only be added if they are of the same type. Also, we should keep in mind that the sign of the term becomes the opposite when sent on the other side of the “ $ = $ ” sign.
Now we’ll add the constants associated with the variables, ignoring the variable part.
 \[ \Rightarrow 15x = 90\]
To obtain the value of $ x $ , we have to divide both the sides by $ 15 $ .
 $ \Rightarrow x = \dfrac{{90}}{{15}} $
By simplifying the above equation we get,
 $ \Rightarrow x = 6 $
Hence, it is the required value of $ x $ .
Alternate method:
We are given,
 \[5x + 10x = 90\]
Now we’ll add the constants associated with the variables, ignoring the variable part.
 \[ \Rightarrow 15x = 90\]
Now we’ll transpose the terms. Transposing terms converts operation into inverse operation when sent to the other side of the operation. Addition becomes Subtraction and vice versa. Multiplication becomes Division and vice versa.
 $ \Rightarrow x = \dfrac{{90}}{{15}} $
By simplifying the above equation we get,
 $ \Rightarrow x = 6 $
Hence, it is the required value of $ x $ .
So, the correct answer is “x = 6”.

Note: The operations like addition, subtraction, multiplication and division can only be performed on like terms. To solve questions which have both variables and constants, keep in mind to solve them separately i.e. constants are to be dealt with constants and variables are to be dealt with variables. In case of variables, their coefficients are operated.