Question

Step-by-step how-to evaluation

Answer 1

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

Distribution property
$\boxed{a(b+c) = ab+ac}$

$126( \frac{8}{9}+ \frac{x-4}{7} )$
$=126( \frac{8}{9} )+126( \frac{x-4}{7})$
$= \frac{126(8)}{9} + \frac{126(x-4)}{7}$


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.
$= \boxed{\frac{126(8)}{9}} + \frac{126(x-4)}{7}$
$= \boxed{\frac{14(8)}{1}} + \frac{126(x-4)}{7}$
$= 14(8) + \frac{126(x-4)}{7}$

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.
$=14(8) + \boxed{\frac{126(x-4)}{7}}$
$=14(8) + \boxed{\frac{18(x-4)}{1}}$
$=14(8)+18(x-4)$


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