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

Solve 2x75 X310 X115find The Value Of X And Verify The Result Will RHS class=

Sagot :

SalmonWorldTopper

Step-by-step explanation:

Given Question :-

Solve for x :-

[tex] \dfrac{2x + 7}{5} - \dfrac{x - 3}{10} = \dfrac{x + 1}{15} [/tex]

[tex] \red{\large\underline{\sf{Solution-}}}[/tex]

Given linear equation is

[tex]\rm :\longmapsto\: \dfrac{2x + 7}{5} - \dfrac{x - 3}{10} = \dfrac{x + 1}{15} [/tex]

[tex]\rm :\longmapsto\: \dfrac{2(2x + 7) - (x - 3)}{10} = \dfrac{x + 1}{15} [/tex]

[tex]\rm :\longmapsto\: \dfrac{4x + 14 - x + 3}{10} = \dfrac{x + 1}{15} [/tex]

[tex]\rm :\longmapsto\: \dfrac{(4x - x) + (14 + 3)}{10} = \dfrac{x + 1}{15} [/tex]

[tex]\rm :\longmapsto\: \dfrac{3x + 17}{10} = \dfrac{x + 1}{15} [/tex]

On multiply by 5 on both sides,

[tex]\rm :\longmapsto\: \dfrac{3x + 17}{2} = \dfrac{x + 1}{3} [/tex]

On cross multiplication, we get

[tex]\rm :\longmapsto\:3(3x + 17) = 2(x + 1)[/tex]

[tex]\rm :\longmapsto\:9x +51 = 2x + 2[/tex]

[tex]\rm :\longmapsto\:9x - 2x = 2 - 51 [/tex]

[tex]\rm :\longmapsto\:7x = - 49[/tex]

[tex]\bf\implies \:x = - 7[/tex]

VERIFICATION

Consider, LHS

[tex]\red{\rm :\longmapsto\: \dfrac{2x + 7}{5} - \dfrac{x - 3}{10}}[/tex]

On substituting the value of x, we get

[tex]\red{\rm \:  =  \: \dfrac{2( - 7) + 7}{5} - \dfrac{ - 7 - 3}{10}}[/tex]

[tex]\red{\rm \:  =  \: \dfrac{ - 14 + 7}{5} - \dfrac{ - 10}{10}}[/tex]

[tex]\red{\rm \:  =  \: \dfrac{ - 7}{5} + 1}[/tex]

[tex]\red{\rm \:  =  \: \dfrac{ - 7 + 5}{5}}[/tex]

[tex]\red{\rm \:  =  \: \dfrac{ - 2}{5}}[/tex]

Consider RHS

[tex] \green{\rm :\longmapsto\:\dfrac{x + 1}{15}}[/tex]

On substituting the value of x, we get

[tex] \green{\rm \:  =  \: \dfrac{ - 7 + 1}{15}}[/tex]

[tex] \green{\rm \:  =  \: \dfrac{ - 6}{15}}[/tex]

[tex] \green{\rm \:  =  \: \dfrac{ - 2}{5}}[/tex]

[tex]\rm \implies\:LHS=RHS[/tex]

HENCE, VERIFIED

Answer:

Step-by-step explanation:

100+5

105

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