Question

How do you solve: $ 10x + 5 = 20 - 20x $ ?

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 the following equation by writing the like terms together i.e. all the variables together and constants together.

Complete step by step solution:
We are given,
 $ \Rightarrow 10x + 5 = 20 - 20x $
Firstly, we have to bring the like terms together and rewrite the equation to solve the question. As we know that two numbers can only be added if they are of same type. Also, we need to keep in mind that sign of the term becomes opposite when sent on the other side of “ $ = $ ” sign
 $ \Rightarrow 10x + 20x = 20 - 5 $
Now you have to add the constants associated with the variables, ignoring the variable part.
 $ \Rightarrow 30x = 15 $
To obtain the value of $ x $ , we have to divide both the sides by 30.
 $ \Rightarrow x = \dfrac{{15}}{{30}} $
By simplifying the above equation we get,
 $ \Rightarrow x = \dfrac{{15}}{{30}} $
Hence, it is the required value of $ x $ .
Alternative method-
We are given,
 $ \Rightarrow 10x + 5 = 20 - 20x $
We’ll subtract $ 5 $ from both the sides, to eliminate numeric term from LHS
 $ \Rightarrow 10x + 5 - 5 = 20 - 20x - 5 $
 $ \Rightarrow 10x = 15 - 20x $
To eliminate variable term from RHS, we’ll add $ 20x $ on both the sides
 $ \Rightarrow 10x + 20x = 15 - 20x + 20x $
 $ \Rightarrow 30x = 15 $
By simplifying the above equation we get,
 $ \Rightarrow x = \dfrac{1}{2} $
So, the correct answer is “ $ x = \dfrac{1}{2} $ ”.

Note: Operations such as 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 dealt with constants and variables are dealt with variables. In case of variables, their coefficients are operated.