Question

1\2(2x-3)-1\6(2x-5)=6

Answer 1

$\textbf{Solution -}$

$\dfrac{1}{2} (2x - 3) - \dfrac{1}{6} (2x - 5) = 6 \\ \\ \implies \: x - \dfrac{3}{2} - \dfrac{x}{3} + \dfrac{5}{6} = 6 \\ \\ \implies \dfrac{6x - 9 - 2x + 5}{6} = 6 \\ \\ \implies \: (6x - 2x) + ( - 9 + 5) = 6 \times 6 \\ \\ \implies \: 4x - 4 = 36 \\ \\ \: \implies4x = 36 + 4 \\ \\ \implies \: 4x = 40 \\ \\ \implies \: x = \dfrac{ \cancel{40}}{ \cancel{4}} 10 \\ \\ \implies \: x = 10$

Hence, the value of $\textbf{x = 10}$.

$\textbf{\underline{Some things to know :}}$

$\bullet \: {\textbf{Transposition :}}$ It is the process of transferring a number or value from one side to another side and the sign get's changed.

e.g.

$\dfrac{a}{b} = 1 \\ \\ \Rightarrow a = b$

$\bullet \: {\textbf {Signs :}}$

(+) (+) = (+)

(-) (-) = (+)

(-) (+) = (-)

(+) (-) = (-)

✪ $\textbf{Be Brainly}$ ✪

Answer 2

Step-by-step explanation:

$Solution \\\\\begin{gathered} \dfrac{1}{2} (2x - 3) - \dfrac{1}{6} (2x - 5) = 6 \\ \\ \implies \: x - \dfrac{3}{2} - \dfrac{x}{3} + \dfrac{5}{6} = 6 \\ \\ \implies \dfrac{6x - 9 - 2x + 5}{6} = 6 \\ \\ \implies \: (6x - 2x) + ( - 9 + 5) = 6 \times 6 \\ \\ \implies \: 4x - 4 = 36 \\ \\ \: \implies4x = 36 + 4 \\ \\ \implies \: 4x = 40 \\ \\ \implies \: x = \dfrac{ \cancel{40}}{ \cancel{4}} 10 \\ \\ \implies \: x = 10 \end{gathered}21(2x−3)−61(2x−5)=6⟹x−23−3x+65=6⟹66x−9−2x+5=6⟹(6x−2x)+(−9+5)=6×6⟹4x−4=36⟹4x=36+4⟹4x=40⟹x=44010⟹x=10</p><p>$