Question

5x/3-(x-1)/2=x-2/3 Transposition method ​

Answer 1

Given: $5x/3-(x-1)/2=x-2/3$

We have to solve the above data.

• For this first, we will Identify the variables and constants in the given equation.
• And then we Simplify the equation in LHS and RHS.
• Then we will transpose or shift the term on the other side to solve the equation further simplest.
• After that, we will Simplify the equation using arithmetic operation as required that is mentioned in the above rule of the linear equations.
• Then the result will be the solution for the given linear equation.

Now by using the transposition method:

We have,

$5x/3-(x-1)/2=x-2/3$

$=>\frac{5 x}{3}-1 \cdot \frac{(x-1)}{2}=x-1 \cdot \frac{2}{3}\\\\\begin{array}{l}=>\frac{5 x}{3}-\frac{x-1}{2}=x-1 \cdot \frac{2}{3} \\\\=>\frac{2 \cdot 5 x}{6}+\frac{3(-(x-1))}{6}=x-1 \cdot \frac{2}{3}\end{array}$

Combining fractions with a common denominator:

$=>\frac{2 \cdot 5 x+3(-(x-1))}{6}=x-1 \cdot \frac{2}{3}\\\\=>\frac{10 x+3(-(x-1))}{6}=x-1 \cdot \frac{2}{3}$

$=>\frac{10 x+3(-x+1)}{6}=x-1 \cdot \frac{2}{3}\\\\=>\frac{10 x-3 x+3}{6}=x-1 \cdot \frac{2}{3}\\\\=>\frac{7 x+3}{6}=x-1 \cdot \frac{2}{3}\\\\=>\frac{7 x+3}{6}=x-\frac{2}{3}$

Subtracting    from both sides of the equation:

$=>\frac{7 x+3}{6}-x=x-\frac{2}{3}-x\\\\=>\frac{x+3}{6}=-\frac{2}{3}$

Multiplying all terms by the same value to eliminate fraction denominators:

$=>6 \cdot \frac{x+3}{6}=6\left(-\frac{2}{3}\right)\\\\=>x+3=6\left(-\frac{2}{3}\right)\\\\=>x+3=-4\\\\=>x=-4-3\\=>x=-7$

Hence, we get the solution is$x=-7$.

NOTE: In this problem, we are assuming that we have to solve the given equation.

Q. Solve 5x/3-(x-1)/2=x-2/3  using the Transposition method.

Answer 2

To find : value of $x$

Given : $\frac{5x}{3}-\frac{(x-1 )}{2} = x - \frac{2}{3}$

Solution :

• Here, we will use the below following steps to find a solution using the transposition method:

1. We will Identify the variables and constants in the given equation.
2. Then we differentiate the equation as LHS and RHS.
3. We take constants at RHS leaving variable at LHS.  
4. Simplify the equation using arithmetic operation as required to find the value of $x$ .
5. Then the result will be the solution for the given linear equation. By using the transposition method. we get,

• $\frac{5x}{3}-\frac{(x-1 )}{2} = x - \frac{2}{3}$  

      $\Rightarrow \frac{10x -3x + 3 }{6} = x -\frac{2}{3} \\\Rightarrow \frac{7x+3}{6}-x = - \frac{2}{3} \\\Rightarrow \frac{7x + 3-6x}{6} =\frac{-2}{3} \\\Rightarrow \frac{x + 3}{6} = \frac{-2}{3} \\\Rightarrow 3 ( x + 3 ) =-12 \\\Rightarrow 3x + 9 = -12 \\\Rightarrow 3x = -21\\\Rightarrow x = -7$

 Hence, value of $x$ is $-7$  .

Note : since value of $x$ was not given therefore on solving by transposition method we get  value of $x$  .