Question

10x+(9-x)+27=10(9-x)+x

Answer 1

$10x+(9-x)+27=10(9-x)+x\\\\10x+9-x+27=90-10x+x\\\\9x+36=90-9x\\\\9x+9x=90-36\\\\18x=54\\\\\\x= \frac{54}{18} \\x=3$

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Answer 2

❥$\:\:\Large\sf\red{\underline{\underline{Given}}}\::$

• $\small\bf \gray { 10x + (9 - x) + 27 = 10(9 - x) + x}$

❥$\:\:\Large\sf\green{\underline{\underline{To \ Find}}}\::$

• $\bf\gray{Value \ of \ x}$

❥$\:\:\Large\sf\pink{\underline{\underline{Solution}}}\::$

${\red{\leadsto}}\:\:\bf\purple{10x \ + \ (9 \ - \ x) \ + \ 27 \ = \ 10(9 \ - \ x) \ + \ x}$

$\bf\underline\orange{Collect \ and \ combine \ like \ terms }$

${\red{\leadsto}}\:\:\bf\blue{9x \ + \ 36 \ = \ 10 \ . \ (9x \ - \ x) \ + \ x}$

$\bf\underline\orange{Simplify \ right \ side}$

${\red{\leadsto}}\:\:\bf\purple{9x \ + \ 36 \ = \ -9x \ + \ 90}$

$\bf\underline\orange{Add \ to \ both \ sides}$

${\red{\leadsto}}\:\:\bf\blue{(9x \ + \ 36) \ + \ 9x \ = \ ( -9x \ + \ 90) \ + \ 9x}$

$\bf\underline\orange{Again \ collect \ and \ combine \ like \ terms }$

${\red{\leadsto}}\:\:\bf\purple{18x \ + \ 36 \ = \ ( -9x \ + \ 90) \ + \ 9x}$

$\bf\underline\orange{Simplify \ right \ side}$

${\red{\leadsto}}\:\:\bf\blue{18x \ + \ 36 \ = \ 90}$

$\bf\underline\orange{Subtract \ from \ both \ sides}$

${\red{\leadsto}}\:\:\bf\purple{(18x \ + \ 36) \ - \ 36 \ = \ 90 \ - \ 36}$

$\bf\underline\orange{Simplify \ left \ side}$

${\red{\leadsto}}\:\:\bf\blue{18x \ = \ 90 \ - \ 36}$

$\bf\underline\orange{Simplify \ arithmetic}$

${\red{\leadsto}}\:\:\bf\purple{18x \ = \ 54}$

$\bf\underline\orange{Divide \ from \ both \ sides }$

${\red{\leadsto}}\:\:\bf\blue{\dfrac{18x}{18} \ = \ \dfrac{54}{18}}$

$\bf\underline\orange{Fraction \ cancellation }$

${\red{\leadsto}}\:\:\bf\purple{x \ = \ \dfrac{\cancel{54}}{\cancel{18}}}$

$\bf\underline\orange{Final \ Answer }$

❥$\:\:\underline{\boxed{\bf{\red{x \ = \ 3}}}}$