Question

$\frac{3}{4} ( \frac{7x - 1}{4} ) - (2x - \frac{1 - x}{2} ) = x + 11$
class 8 Mathematics CBSE Manjit Singh
solve it in easy way so that I could get
answer is
$- \frac{171}{35}$
it's answer show me way of the question and Do not spam me​

Answer 1

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

Given linear equation is

$\rm :\longmapsto\:\dfrac{3}{4} \bigg( \dfrac{7x - 1}{4}\bigg) - \bigg(2x - \dfrac{1 - x}{2}\bigg) = x + 11$

can be rewritten as

$\rm :\longmapsto\: \dfrac{21x - 3}{16} - \bigg( \dfrac{4x - (1 - x)}{2}\bigg) = x + 11$

$\rm :\longmapsto\: \dfrac{21x - 3}{16} - \bigg( \dfrac{4x - 1 + x}{2}\bigg) = x + 11$

$\rm :\longmapsto\: \dfrac{21x - 3}{16} - \bigg( \dfrac{5x - 1}{2}\bigg) = x + 11$

$\rm :\longmapsto\: \dfrac{21x - 3}{16} - \dfrac{5x - 1}{2} = x + 11$

$\rm :\longmapsto\: \dfrac{21x - 3 - 8(5x - 1)}{16} = x + 11$

$\rm :\longmapsto\: \dfrac{21x - 3 - 40x + 8}{16} = x + 11$

$\rm :\longmapsto\: \dfrac{5 - 19x}{16} = x + 11$

$\rm :\longmapsto\:5 - 19x = 16(x + 11)$

$\rm :\longmapsto\:5 - 19x = 16x + 176$

$\rm :\longmapsto\: - 19x - 16x = 176 - 5$

$\rm :\longmapsto\: - 35x = 171$

$\rm \implies\:\boxed{ \tt{ \: x \: = \: - \: \frac{171}{35} \: }}$

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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

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

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

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

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