Question

Step-by-step how-to evaluation

Answer 1

First, we can use distribution property to simplify the expression.

Distribution property

`\boxed{a(b+c) = ab+ac}`


`126( (8)/(9)+ (x-4)/(7) )`

`=126( (8)/(9) )+126( (x-4)/(7))`

`= (126(8))/(9) + (126(x-4))/(7)`


Second, simplify the numerator and the denominator
Because the numerator (126) and the denominator (9) on the first term has 9 as the greatest common factor, divide the numerator and the denominator by 9.

`= \boxed{(126(8))/(9)} + (126(x-4))/(7)`

`= \boxed{(14(8))/(1)} + (126(x-4))/(7)`

`= 14(8) + (126(x-4))/(7)`

Because the numerator (126) and the denominator (7) on the second term has 7 as the greatest common factor, divide the numerator and the denominator by 7.

`=14(8) + \boxed{(126(x-4))/(7)}`

`=14(8) + \boxed{(18(x-4))/(1)}`

`=14(8)+18(x-4)`


Third, simplify the first term by multiplication, simplify the second term by distribution property
= 14(8) + 18(x - 4)
= 112 + 18(x - 4)
= 112 + 18x - 18(4)
= 112 + 18x - 72

add the constant (112) with the other constant (-72)
= 18x + 112 - 72
= 18x + 40


This is the simplest expression

`\boxed{18x+40}`

Answer 2

Least common multiple=lcm
lcm(9,7)=63

126(8/9 + (x-4)/7 )=
126(7*8+9(x-4)/63=
126(56+9x-36)/63=
126(20+9x)/63= (126/63=2)
2(20+9x)=
40+18x

Answer: 126(8/9 + (x-4)/7 )= 40+18x