Question

HELP When 2((Three-fifths x + 2 and three-fourths y minus one-fourth x minus 1 and one-half y + 3)) is simplified, what is the resulting expression? 1 and StartFraction 7 over 10 EndFraction x + 2 and one-half y + 6 StartFraction 7 over 10 EndFraction x + 2 and one-half y + 6 StartFraction 7 over 10 EndFraction x + 8 and one-half y + 6 1 and StartFraction 7 over 10 EndFraction x + 4 and one-fourth y + 3

Answer 1

StartFraction 7 over 10 EndFraction x + 2 and one-half y + 6

Explanation:

Given the expression
`2((3x)/(5)+2(3y)/(4)-(x)/(4)-1 (1)/(2)y+3)`

To simplify the expression, we need to first collect the like terms of the functions in parentheses as shown;

`= 2((3x)/(5)-(x)/(4)-1 (1)/(2)y+2(3)/(4)y+3)\\= 2((3x)/(5)-(x)/(4)- (3)/(2)y+(11)/(4)y+3)\\`

Then we find the LCM of the resulting function

`= 2((3x)/(5)-(x)/(4)- (3)/(2)y+(11)/(4)y+3)\\= 2((12x-5x)/(20) - ((6y-11y)/(4))+3)\\= 2((7x)/(20)- ((-5y)/(4))+3 )\\= 2((7x)/(20)+ (5y)/(4)+3 )\\= (7x)/(10) + (5y)/(2) +6\\= (7x)/(10) + 2(1)/(2)y+6\\`

The final expression gives the required answer