Question

solving linear equation using rule of transposition.
3(5x-2)-4(x+4)=7(x-1)-1​

Answer 1

Basic Concept Used :-

Transposition is a method to isolate the variable to one side of the equation and everything else to the other side so that you can solve the equation.

We can use the following steps to find a solution using transposition method:

• Step 1) Identify the variables and constants in the given simple equation.

• Step 2) Simplify the equation in and .

• Step 3) Transpose the term on the other side to solve the equation further simplest.

• Step 4) Simplify the equation using arithmetic operation as required that is mentioned in rule 1 or rule 2 of linear equations.

• Step 5) Then the result will be the solution for the given linear equation.

Let's solve the problem now!!

$\large\underline{\sf{Solution-}}$

$\rm :\longmapsto\:3(5x-2)-4(x+4)=7(x-1)-1$

$\rm :\longmapsto\:15x - 6 - 4x - 16 = 7x - 7 - 1$

$\rm :\longmapsto\:11x - 22 = 7x - 8$

$\rm :\longmapsto\:11x - 7x = - 8 + 22$

$\rm :\longmapsto\:4x = 14$

$\bf\implies \:x \: = \: \dfrac{7}{2}$

Verification :-

• Consider LHS

$\rm :\longmapsto\:3(5x-2)-4(x+4)$

$\: \: \: = \: \: 3\bigg(5 \times \dfrac{7}{2} - 2\bigg) - 4\bigg( \dfrac{7}{2} + 4\bigg)$

$\: \: \: = \: \: 3\bigg(\dfrac{35}{2} - 2\bigg) - 4\bigg(\dfrac{7 + 8}{2} \bigg)$

$\: \: \: = \: \: 3\bigg(\dfrac{35 - 4}{2}\bigg) - 2 \times 15$

$\: \: \: = \: \: 3\bigg(\dfrac{31}{2}\bigg) - 30$

$\: \: \: = \: \: \dfrac{93}{2} - 30$

$\: \: \: = \: \: \dfrac{93 - 60}{2}$

$\: \: \: = \: \: \dfrac{33}{2}$

Now,

• Consider RHS,

$\rm :\longmapsto\:7(x - 1) - 1$

$\: \: \: = \: \: 7\bigg(\dfrac{7}{2} - 1\bigg) - 1$

$\: \: \: = \: \: 7\bigg(\dfrac{7 - 2}{2} \bigg) - 1$

$\: \: \: = \: \: 7\bigg(\dfrac{5}{2} \bigg) - 1$

$\: \: \: = \: \: \dfrac{35}{2} - 1$

$\: \: \: = \: \: \dfrac{35 - 2}{2}$

$\: \: \: = \: \: \dfrac{33}{2}$

LHS = RHS

Hence, Verified