Question

X-1/5 + x-2/2 = x/3 + 1

Answer 1

$\textbf{Given:}$

$\mathsf{\dfrac{x-1}{5}+\dfrac{x-2}{2}=\dfrac{x}{3}+1}$

$\textbf{To find:}$

$\textsf{Solution of the given equation}$

$\textbf{Solution:}$

$\textsf{Consider,}$

$\mathsf{\dfrac{x-1}{5}+\dfrac{x-2}{2}=\dfrac{x}{3}+1}$

$\implies\mathsf{\dfrac{2(x-1)+5(x-2)}{10}=\dfrac{x+3}{3}}$

$\implies\mathsf{\dfrac{2x-2+5x-10}{10}=\dfrac{x+3}{3}}$

$\implies\mathsf{\dfrac{7x-12}{10}=\dfrac{x+3}{3}}$

$\implies\mathsf{3(7x-12)=10(x+3)}$

$\implies\mathsf{21x-36=10x+30}$

$\implies\mathsf{21x-10x=30+36}$

$\implies\mathsf{11x=66}$

$\implies\mathsf{x=\dfrac{66}{11}}$

$\implies\boxed{\mathsf{x=6}}$

$\textbf{Answer:}$

$\mathsf{Solution\;is\;x=6}$

$\textbf{Find more:}$

3x-(y+7)/11+2=10 , 2y+(x+11)/7=10 

Solve for x and y

https://brainly.in/question/5587886

Answer 2

Step-by-step explanation:

$\frac{x - 1}{5} + \frac{x - 2}{2} = \frac{x}{3} + 1 \\ \frac{2(x - 1) + 5(x - 2)}{5 \times 2} = \frac{x + 3}{3} \\ \frac{2x - 2 + 5x - 10}{10} = \frac{x + 3}{3} \\ \frac{7x - 12}{10} = \frac{x + 3}{3} \\ 3(7x - 12) = 10(x + 3) \\ 21x - 36 = 10x + 30 \\ 21x - 10x = 30 + 36 \\ 11x = 66 \\ x = \frac{ \cancel{ 66}_{ \: \: 6}}{ \cancel{ 11}_{ \: \: 1} } \\ \boxed{ \large x = \underline{ \underline{6}}}$