Question

Linear equation
Please anyone help
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Answer 1

Answer:

2(2x+7)-x+3/10=x+1/15

4x+14-x+3/10=x+1/15

3x+17/10=x+1/15

15(3x+17)=10(x+1)

45x+255=10x+10

45x-10x=10-255

35x=244

x=244/35

Answer 2

Given Question :-

Solve for x :-

$\dfrac{2x + 7}{5} - \dfrac{x - 3}{10} = \dfrac{x + 1}{15}$

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

Given linear equation is

$\rm :\longmapsto\: \dfrac{2x + 7}{5} - \dfrac{x - 3}{10} = \dfrac{x + 1}{15}$

$\rm :\longmapsto\: \dfrac{2(2x + 7) - (x - 3)}{10} = \dfrac{x + 1}{15}$

$\rm :\longmapsto\: \dfrac{4x + 14 - x + 3}{10} = \dfrac{x + 1}{15}$

$\rm :\longmapsto\: \dfrac{(4x - x) + (14 + 3)}{10} = \dfrac{x + 1}{15}$

$\rm :\longmapsto\: \dfrac{3x + 17}{10} = \dfrac{x + 1}{15}$

On multiply by 5 on both sides,

$\rm :\longmapsto\: \dfrac{3x + 17}{2} = \dfrac{x + 1}{3}$

On cross multiplication, we get

$\rm :\longmapsto\:3(3x + 17) = 2(x + 1)$

$\rm :\longmapsto\:9x +51 = 2x + 2$

$\rm :\longmapsto\:9x - 2x = 2 - 51$

$\rm :\longmapsto\:7x = - 49$

$\bf\implies \:x = - 7$

VERIFICATION

Consider, LHS

$\red{\rm :\longmapsto\: \dfrac{2x + 7}{5} - \dfrac{x - 3}{10}}$

On substituting the value of x, we get

$\red{\rm \:  =  \: \dfrac{2( - 7) + 7}{5} - \dfrac{ - 7 - 3}{10}}$

$\red{\rm \:  =  \: \dfrac{ - 14 + 7}{5} - \dfrac{ - 10}{10}}$

$\red{\rm \:  =  \: \dfrac{ - 7}{5} + 1}$

$\red{\rm \:  =  \: \dfrac{ - 7 + 5}{5}}$

$\red{\rm \:  =  \: \dfrac{ - 2}{5}}$

Consider RHS

$\green{\rm :\longmapsto\:\dfrac{x + 1}{15}}$

On substituting the value of x, we get

$\green{\rm \:  =  \: \dfrac{ - 7 + 1}{15}}$

$\green{\rm \:  =  \: \dfrac{ - 6}{15}}$

$\green{\rm \:  =  \: \dfrac{ - 2}{5}}$

$\rm \implies\:LHS=RHS$

HENCE, VERIFIED