Question

(i) 5(y-3) = 3(2y+1)
iii) 4(22-3)+3 = 2(z+3)-3(z+1)
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Answer 1

$\Large\underline{\bf \orange{Case \: 1 :}}$

$\tt \implies5(y - 3) = 3(2y + 1) \\ \\ \tt \implies 5y - 15 = 6y + 3 \\ \\ \tt \implies 5y - 6y = 3 + 15 \\ \\ \tt \implies - y = 18 \\ \\ \tt \implies y = - 18$

$\Large\underline{\bf \orange{Case \: 2 :}}$

$\tt \implies4(22 - 3) + 3 = 2(z + 3) - 3(z + 1) \\ \\\tt \implies 4(19) + 3 = 2z + 6 - 3z - 3 \\ \\\tt \implies 76 + 3 = 2z - 3z - 3 + 6 \\ \\ \tt \implies79 = - z + 3 \\ \\ \tt \implies - z = 79 - 3 \\ \\\tt \implies - z = 76 \\ \\ \tt \implies z = - 76$

Answer 2

⠀

$\huge{\underline{\underline{\sf{\blue{SOLUTION:-}}}}}$

⠀

$\sf{\underline{\green{Given:-}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• (i) 5(y - 3 ) = 3(2y + 1)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\sf{\underline{\green{Explanation:-}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\:\:\:\:\sf {5(y - 3) = 3(2y + 1)}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\longrightarrow \sf {5y - 15 = 6y + 3 }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\longrightarrow \sf {5y - 6y = 3 + 15 }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\longrightarrow \sf {-y = 18 }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\longrightarrow{\gray{ \underbrace{\boxed{\underline{\underline{\blue{ \tt y = -18}}}}}}}$

$\rule{200}{2}$

⠀

$\sf{\underline{\green{Given:-}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• (ii) 4(22 - 3) + 3 = 2(z + 3) - 3(z + 1)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\sf{\underline{\green{Explanation:-}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\:\:\:\:\sf {4(22 - 3) + 3 = 2(z + 3) - 3(z + 1)}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\longrightarrow \sf {4 \times (19) + 3 = 2z + 6 - 3z - 3 }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\longrightarrow \sf {76 + 3 = 2z - 3z - 3 + 6 }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\longrightarrow \sf {79 = -z + 3}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\longrightarrow \sf {-z = 79 - 3}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\longrightarrow \sf {-z = 76}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\longrightarrow{\gray{ \underbrace{\boxed{\underline{\underline{\blue{ \tt z = -76}}}}}}}$

$\rule{200}{2}$