Question

1/2r + 2(3/4r - 1) = 1/4r + 6

Answer 1

`(1)/(2)r+2((3)/(4)r-1)=(1)/(4)r+6\\\\(1)/(2)r+2*(3)/(4)r-2\cdot1=(1)/(4)r+6\\\\(1)/(2)r+(3)/(2)r-2=(1)/(4)r+6\\\\(1+3)/(2)r-2=(1)/(4)r+6\\\\(4)/(2)r-2=(1)/(4)r+6\\\\2r-2=(1)/(4)r+6\ \ \ \ \ \ |add\ 2\ to\ both\ sides\\\\2r=(1)/(4)r+8\ \ \ \ |subtract\ (1)/(4)r\ from\ both\ sides`


`1(3)/(4)r=8\\\\(1\cdot4+3)/(4)r=8\\\\(7)/(4)r=8\ \ \ \ \ |divide\ both\ sides\ by\ (7)/(4)\ (multiply\ both\ sides\ by\ (4)/(7))\\\\r=8\cdot(4)/(7)\\\\r=(8\cdot4)/(7)\\\\r=(32)/(7)\\\\\boxed{r=4(4)/(7)}`

Answer 2

`(1)/(2)r+2((3)/(4)r-1)=(1)/(4)r+6\ \ \ \ \ \ \ |omit\ bracket\\\\(1)/(2)r+(3)/(2)r-2=(1)/(4)r+6\ \ \ \ \ \ |\cdot4\\\\2r+6r-8=r+24\ \ \ \ \ \ |combine\ like\ terms\\\\2r+6r-r=24+8\ \ \ \ \ |simplify\\\\7r=32\ \ \ \ \ |:7\\\\r=(32)/(7)=4(4)/(7)`