Question

Ch. SIMPLE LINEAR EQUATIONS. Step by step ​

Answer 1

$\huge\underline\bold\red {Answer = 10}$

$\frac{3x - 2}{7} - \frac{x - 2}{4} = 2$

$\frac{12x - 8}{28} - \frac{7x - 2}{28} = 2$

$\frac{5x - 6}{28} = 2$

$5 x - 6 = 2 \times 28$

$5x - 6 = 56$

$5x = 56 - 6$

$5x = 50$

$x = \frac{50}{5}$

$\fbox\blue{x = 10}$

$\huge\overbrace\green {Value\: of\: x\: is \:10}$

Answer 2

Given :-

$\: \: \: \: \: \: \: \: \: \bull \: \:{ \sf{ \cfrac{3x - 2}{7} - \cfrac{x - 2}{4} = 2 }}$

To find :-

• Value of x.

Solution :-

${ \implies{ \sf{ \cfrac{3x - 2}{7} - \cfrac{x - 2}{4} = 2 }}}$

Finding LCM of 7 and 4 by factorization method.

》7 = 7 × 1

》4 = 2 × 2

LCM of 7 and 4 is

》7 × 2 × 2

》7 × 4

》28

For making the Denominator common we have to multiply but numbers by 4 and 7 respectively that will become 28.

${ \implies{ \sf{ \cfrac{4(3x - 2)}{7 \times 4} - \cfrac{7(x - 2)}{4 \times 7} = 2 }}} \\\\{ \implies{ \sf{ \cfrac{4(3x - 2)}{28} - \cfrac{7(x - 2)}{28} = 2 }}} \\\\{ \implies{ \sf{ \cfrac{(12x - 8)}{28} - \cfrac{(7x - 14)}{28} = 2 }}}$

Now Denominator is same, so we can take it as common.So,

${ \implies{ \sf{ \cfrac{(12x - 8) -(7x - 14 )}{28} = 2 }}}$

While opening the Bracket all sign changes If and only if there will minus sign before the bracket. So,

${ \implies{ \sf{ \cfrac{12x - 8 -7x + 14 }{28} = 2 }}}$

${ \implies{ \sf{ \cfrac{12x - 7x -8 + 14 }{28} = 2 }}}$

${ \implies{ \sf{ \cfrac{5x + 6}{28} = 2 }}}$

In left side 28 is in Division form. On transfering 28 on right side it will be multiplied by 2. So,

$\\ { \implies{ \sf{ {5x + 6}= 2 \times 28 }}}$

$\\ { \implies{ \sf{ {5x + 6}= 56}}}$

Remember while solving that sign will be placed of greater number only.

$\\ { \implies{ \sf{ {5x }= 56 - 6}}}$

$\\ { \implies{ \sf{ {5x }= 50}}}$

${ \implies{ \sf{ {x }= \cfrac{50}{5} }}}$

$\Large{ \underline{ \boxed{ \red { \implies{ \sf{ {x }= 10 }}} }}}$