Question

Solve the equation:
12-x/5=x

Answer 1

Hey There!

Sheena Here!

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Your question: Solve the equation:  12-x/5=x

So, Before I explain the solution, lets have a quick intro with some terms

Linear Equations - Equations which should have a variable, a constant and an equal to '=' sign.

Variable- The unknown value which we are told to find is termed as variable. Variable are denoted with any letter be it 'x' or 'y' , but they must be in small letter.

Constant - The fixed value we have in the equation is the constant

Method of Transposing- Its a Method used in solving equation where we take the number from LHS to RHS and the signs gets changed.

Follow this table for changing the signs when you transpose a number which is like in following cases from LHS (Left hand side) to RHS (Right hand side) and vice-versa.

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LHS               RHS

+                     -

*                     ÷

²                    √

³                    ∛

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These were the most commonly used signs.

Solution:

So, Here there's a variable 'x'

In this equation it means that a number x/5 is subtracted from 12 and the resulting difference is x. That means if x = numerator then the difference is the same number which is in the numerator.

So, Lets use the method of transposition.

12 - x/5 = x

∴ 12 = x + x/5

(Use the above information to know the conversion of sign, here - turned to +)

12 = x + x/5

12 = x*5 /1*5 + x/5 (Cross multiplication

12 = 5x/5 +x/5

12 = 6x/5

12 * 5 = 6x

(Use the above information to know the conversion of sign, here ÷ turned to *)

60 = 6x i.e 6*x

60/6 = x

(Use the above information to know the conversion of sign, here * turned to ÷)

10 = x

therefore, the solution of the equation is x= 10

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Verification:

12 - x/5 = x

12 - 10/5 = 10

LHS            RHS

12 - 2   =      10

10         =      10

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Hope this helps!

Thanks!

Answer 2

Answer:

=> x = 10

Step-by-step explanation:

Given that:-

$12-\frac{x}{5} =x$

To find:- The value of the x,

By using the method of transposition,

As we have,

=> $12-\frac{x}{5} =x$

First of all, we have to find the common denominator:

=> $\frac{5\times 12}{5} +\frac{-x}{5}=x$

=> $\frac{5\times 12-x}{5}=x$

=> $\frac{60-x}{5}=x$

Now rearrange the terms,

=> $\frac{-x+60}{5}=x$

Multiply both sides by $5$ in order to eliminate denominator,

=> $\frac{-x+60}{5}\times 5=x\times 5$

=> $-x + 60 = 5x$

Now subtract both sides by $60$, we get

=> $-x + 60-60 = 5x-60$

=> $-x = 5x - 60$

Subtract $5x$ from both sides,

=> $-x -5x= 5x - 60-5x$

=> $-6x = -60$

Divide both sides by $-6$,

=> $x = 10$

Hence, the required solution is 10.