Question

Solve: 2x+7/5 - x-3/10 = x+1/15
find the value of x and verify the result will RHS ​

Answer 1

Explanation:

100+5

105

Answer 2

Explanation:

Given Question :-

Solve for x :-

`(2x + 7)/(5) - (x - 3)/(10) = (x + 1)/(15)`

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

Given linear equation is

`\rm :\longmapsto\: (2x + 7)/(5) - (x - 3)/(10) = (x + 1)/(15)`

`\rm :\longmapsto\: (2(2x + 7) - (x - 3))/(10) = (x + 1)/(15)`

`\rm :\longmapsto\: (4x + 14 - x + 3)/(10) = (x + 1)/(15)`

`\rm :\longmapsto\: ((4x - x) + (14 + 3))/(10) = (x + 1)/(15)`

`\rm :\longmapsto\: (3x + 17)/(10) = (x + 1)/(15)`

On multiply by 5 on both sides,

`\rm :\longmapsto\: (3x + 17)/(2) = (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\: (2x + 7)/(5) - (x - 3)/(10)}`

On substituting the value of x, we get

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

`\red{\rm \:  =  \: ( - 14 + 7)/(5) - ( - 10)/(10)}`

`\red{\rm \:  =  \: ( - 7)/(5) + 1}`

`\red{\rm \:  =  \: ( - 7 + 5)/(5)}`

`\red{\rm \:  =  \: ( - 2)/(5)}`

Consider RHS

`\green{\rm :\longmapsto\:(x + 1)/(15)}`

On substituting the value of x, we get

`\green{\rm \:  =  \: ( - 7 + 1)/(15)}`

`\green{\rm \:  =  \: ( - 6)/(15)}`

`\green{\rm \:  =  \: ( - 2)/(5)}`

`\rm \implies\:LHS=RHS`

HENCE, VERIFIED