Question

Solve
$\frac{6x + 1}{3} + 1 = \frac{x - 3}{6}$
​

Answer 1

Answer:

$x = - 1$

Step-by-step explanation:

Multiplying both sides of the equation by 6

$\frac{6(6x + 1)}{3} + 6 \times 1 = \frac{6(x - 3)}{6} \\ 2(6x + 1) + 6 = x - 3 \\ 12x + 2 + 63x - 3 \\ 12x + 8 = x - 3 \\ 12x - x + 8 = - 3 \\ 11x + 8 = - 3 \\ 11x = - 11 \\ x = - 1$

$Check:LHS = \frac{6( - 1) - 3}{6} + 1 \\= \frac{ - 6 + 1}{3} + 1 \\ = \frac{ - 5}{3} + \frac{3}{3} = \frac{ - 5 + 3}{3} = \frac{ - 2}{3}$

$RHS = \frac{( - 1) - 3}{6} = \frac{ - 4}{6} = \frac{ - 2}{3}$

$LHS=RHS \: (as \: required)$

Answer 2

Answer:

-1

Step-by-step explanation:

$\frac{6x + 1}{3}  + 1 =  \frac{x - 3}{6}$

$\frac{6x+1+3}{3} =\frac{x-3}{6}$

${6x+4}=\frac{x-3}{2}$

$2(6x+4)=x-3$

$12x+8=x-3$

$11x=-11$

$x=-1$