Question

$x+6 by 4+x-3 by 5=5x-4 by8$

Answer 1

Answer:

GIVEN :

The equation is \frac{x+6}{4}+\frac{x-3}{5}=\frac{5x-4}{8}4x+6+5x−3=85x−4

TO FIND :

The solution of the given equation  \frac{x+6}{4}+\frac{x-3}{5}=\frac{5x-4}{8}4x+6+5x−3=85x−4

SOLUTION :

Given equation is  \frac{x+6}{4}+\frac{x-3}{5}=\frac{5x-4}{8}4x+6+5x−3=85x−4

\frac{5(x+6)+4(x-3)}{20}=\frac{5x-4}{8}205(x+6)+4(x−3)=85x−4

Now we have to find the solution for the given equation that is to find the value of x.

By using the Distributive property :

a(x+y)=ax+ay

\frac{5(x)+5(6)+4(x)+4(-3)}{20}=\frac{5x-4}{8}205(x)+5(6)+4(x)+4(−3)=85x−4

\frac{5x+30+4x-12}{20}=\frac{5x-4}{8}205x+30+4x−12=85x−4

\frac{9x+18}{20}=\frac{5x-4}{8}209x+18=85x−4

9x+18=\frac{5x-4}{8}\times 209x+18=85x−4×20

9x+18=\frac{5x-4}{2}\times 59x+18=25x−4×5

(9x+18)\times 2=(5x-4)\times 5(9x+18)×2=(5x−4)×5

By using the Distributive property :

a(x+y)=ax+ay

9x(2)+18(2)=5x(5)-4(5)9x(2)+18(2)=5x(5)−4(5)

18x+36=25x-2018x+36=25x−20

18x+36-25x+20=018x+36−25x+20=0

Adding the like terms we get,

-7x+56=0−7x+56=0

-7x=-56

x=\frac{-56}{-7}x=−7−56

x=8x=8

∴ the value of x in the given equation is 8.