First, we can use distribution property to simplify the expression.
Distribution property
[tex]\boxed{a(b+c) = ab+ac}[/tex]
[tex]126( \frac{8}{9}+ \frac{x-4}{7} )[/tex]
[tex]=126( \frac{8}{9} )+126( \frac{x-4}{7}) [/tex]
[tex]= \frac{126(8)}{9} + \frac{126(x-4)}{7} [/tex]
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.
[tex]= \boxed{\frac{126(8)}{9}} + \frac{126(x-4)}{7}[/tex]
[tex]= \boxed{\frac{14(8)}{1}} + \frac{126(x-4)}{7}[/tex]
[tex]= 14(8) + \frac{126(x-4)}{7}[/tex]
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.
[tex]=14(8) + \boxed{\frac{126(x-4)}{7}}[/tex]
[tex]=14(8) + \boxed{\frac{18(x-4)}{1}}[/tex]
[tex]=14(8)+18(x-4)[/tex]
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
[tex]\boxed{18x+40}[/tex]
