Question

$6(3x + 12) - 5(6x - 1) = 3(x - 8) - 5(7x - 1) + 9$
plz give me answer ​

Answer 1

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

Given linear equation

$\sf :\longmapsto\:6(3x + 12) - 5(6x - 1) = 3(x - 8) - 5(7x - 1) + 9$

↝ First open the braces.

$\sf :\longmapsto\:18x + 72 -30x + 5= 3x - 24 - 35x + 5 + 9$

Rearrange the terms, we get

$\sf :\longmapsto\:18x -30x + 72+ 5= 3x - 35x + 5 + 9 - 24$

$\sf :\longmapsto \: -12x + 77= - 32x - 10$

$\sf :\longmapsto \: -12x + 32x= -77 - 10$

$\sf :\longmapsto \: 20x= -87$

$\bf\implies \:x = - \: \dfrac{87}{20}$

Verification

Given equation is

$\rm :\longmapsto\:6(3x + 12) - 5(6x - 1) = 3(x - 8) - 5(7x - 1) + 9$

Consider LHS

$\rm :\longmapsto\:6(3x + 12) - 5(6x - 1)$

On substituting the value of x, we get

$\rm = \: 6\bigg[ - 3 \times \dfrac{87}{20} + 12\bigg] - 5\bigg[ - 6 \times \dfrac{87}{20} - 1\bigg]$

$\rm = \: 6\bigg[ - \dfrac{261}{20} + 12\bigg] - 5\bigg[ - \dfrac{522}{20} - 1\bigg]$

$\rm = \: 6\bigg[ \dfrac{ - 261 + 240}{20}\bigg] - 5\bigg[ \dfrac{ - 522 - 20}{20} \bigg]$

$\rm = \: 6\bigg[ \dfrac{ - 21}{20}\bigg] - 5\bigg[ \dfrac{ - 542}{20} \bigg]$

$\rm = \: \bigg[ \dfrac{ - 126}{20}\bigg] + \bigg[ \dfrac{2710}{20} \bigg]$

$\rm = \: \dfrac{2584}{20}$

$\rm = \: \dfrac{1292}{10}$

$\rm = \: \dfrac{646}{5}$

Consider RHS

$\rm :\longmapsto\: 3(x - 8) - 5(7x - 1) + 9$

On substituting the value of x, we get

$\rm = \: 3\bigg[ - \dfrac{87}{20} - 8\bigg] - 5\bigg[ - 7 \times \dfrac{87}{20} - 1 \bigg] + 9$

$\rm = \: 3\bigg[ \dfrac{ - 87 - 160}{20}\bigg] - 5\bigg[ \dfrac{ - 609}{20} - 1 \bigg] + 9$

$\rm = \: 3\bigg[ \dfrac{ - 247}{20}\bigg] - 5\bigg[ \dfrac{ - 609 - 20}{20}\bigg] + 9$

$\rm = \: \bigg[ \dfrac{ - 741}{20}\bigg] - 5\bigg[ \dfrac{ - 629}{20}\bigg] + 9$

$\rm = \: \bigg[ \dfrac{ - 741}{20}\bigg] + \bigg[ \dfrac{3145}{20}\bigg] + 9$

$\rm = \: \dfrac{ - 741 + 3145 + 180}{20}$

$\rm = \: \dfrac{ 2584}{20}$

$\rm = \: \dfrac{ 1292}{10}$

$\rm = \: \dfrac{646}{5}$

Hence, LHS = RHS

• HENCE, VERIFIED

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Basic Concept Used :-

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

Step 1 :- dentify the variables and constants in the given linear equation.

Step 2 :- Simplify the equation on both sides by arithmetic operations.

Step 3 :- Transpose the term on the other side to solve the equation in simplest form.

Step 4 :- Simplify the equation using arithmetic operation to separate the variables and constants.

Step 5 :- Then the result will be the solution for the given linear equation.

Keep in mind :- While transposing

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: ( + ) \: changes \: to \: ( - ) \: }}}$

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: ( - ) \: changes \: to \: ( + ) \: }}}$

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: ( \times ) \: changes \: to \: ( \div ) \: }}}$

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: ( \div ) \: changes \: to \: ( \times ) \: }}}$

Answer 2

Answer:

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

Given linear equation

$\sf :\longmapsto\:6(3x + 12) - 5(6x - 1) = 3(x - 8) - 5(7x - 1) + 9$

↝ First open the braces.

$\sf :\longmapsto\:18x + 72 -30x + 5= 3x - 24 - 35x + 5 + 9$

Rearrange the terms, we get

$\sf :\longmapsto\:18x -30x + 72+ 5= 3x - 35x + 5 + 9 - 24$

$\sf :\longmapsto \: -12x + 77= - 32x - 10$

$\sf :\longmapsto \: -12x + 32x= -77 - 10$

$\sf :\longmapsto \: 20x= -87$

$\bf\implies \:x = - \: \dfrac{87}{20}$

Verification

Given equation is

$\rm :\longmapsto\:6(3x + 12) - 5(6x - 1) = 3(x - 8) - 5(7x - 1) + 9$

Consider LHS

$\rm :\longmapsto\:6(3x + 12) - 5(6x - 1)$

On substituting the value of x, we get

$\rm = \: 6\bigg[ - 3 \times \dfrac{87}{20} + 12\bigg] - 5\bigg[ - 6 \times \dfrac{87}{20} - 1\bigg]$

$\rm = \: 6\bigg[ - \dfrac{261}{20} + 12\bigg] - 5\bigg[ - \dfrac{522}{20} - 1\bigg]$

$\rm = \: 6\bigg[ \dfrac{ - 261 + 240}{20}\bigg] - 5\bigg[ \dfrac{ - 522 - 20}{20} \bigg]$

$\rm = \: 6\bigg[ \dfrac{ - 21}{20}\bigg] - 5\bigg[ \dfrac{ - 542}{20} \bigg]$

$\rm = \: \bigg[ \dfrac{ - 126}{20}\bigg] + \bigg[ \dfrac{2710}{20} \bigg]$

$\rm = \: \dfrac{2584}{20}$

$\rm = \: \dfrac{1292}{10}$

$\rm = \: \dfrac{646}{5}$

Consider RHS

$\rm :\longmapsto\: 3(x - 8) - 5(7x - 1) + 9$

On substituting the value of x, we get

$\rm = \: 3\bigg[ - \dfrac{87}{20} - 8\bigg] - 5\bigg[ - 7 \times \dfrac{87}{20} - 1 \bigg] + 9$

$\rm = \: 3\bigg[ \dfrac{ - 87 - 160}{20}\bigg] - 5\bigg[ \dfrac{ - 609}{20} - 1 \bigg] + 9$

$\rm = \: 3\bigg[ \dfrac{ - 247}{20}\bigg] - 5\bigg[ \dfrac{ - 609 - 20}{20}\bigg] + 9$

$\rm = \: \bigg[ \dfrac{ - 741}{20}\bigg] - 5\bigg[ \dfrac{ - 629}{20}\bigg] + 9$

$\rm = \: \bigg[ \dfrac{ - 741}{20}\bigg] + \bigg[ \dfrac{3145}{20}\bigg] + 9$

$\rm = \: \dfrac{ - 741 + 3145 + 180}{20}$

$\rm = \: \dfrac{ 2584}{20}$

$\rm = \: \dfrac{ 1292}{10}$

$\rm = \: \dfrac{646}{5}$

Hence, LHS = RHS

HENCE, VERIFIED

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Basic Concept Used :-

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

Step 1 :- dentify the variables and constants in the given linear equation.

Step 2 :- Simplify the equation on both sides by arithmetic operations.

Step 3 :- Transpose the term on the other side to solve the equation in simplest form.

Step 4 :- Simplify the equation using arithmetic operation to separate the variables and constants.

Step 5 :- Then the result will be the solution for the given linear equation.

Keep in mind :- While transposing

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: ( + ) \: changes \: to \: ( - ) \: }}}$

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: ( - ) \: changes \: to \: ( + ) \: }}}$

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: ( \times ) \: changes \: to \: ( \div ) \: }}}$

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: ( \div ) \: changes \: to \: ( \times ) \: }}}$