Question

Solve for x using common denominators. 4/7 (x+6) = x/(x+6)​

Answer 1

Answer:

The value of x = 4/7

Step-by-step explanation:

Given the expression

$\frac{4}{7\left(x+6\right)}=\frac{x}{x+6}$

$\frac{4}{7\left(x+6\right)}-\frac{x}{x+6}=0$

Multiply the numerator and denominator of $\frac{x}{x+6}$ by 7

$\frac{4}{7\left(x+6\right)}-\frac{7x}{7\left(x+6\right)}=0$

Now taking the denominator $\frac{1}{7\left(x+6\right)}$ as common

$\frac{1}{7\left(x+6\right)}\left(4-7x\right)=0$

$\frac{4-7x}{7\left(x+6\right)}=0$

$\frac{f\left(x\right)}{g\left(x\right)}=0\quad \Rightarrow \quad f\left(x\right)=0$

$4-7x=0$

Subtract 4 from both sides

$4-7x-4=0-4$

Simplify

$-7x=-4$

Divide both sides by -7

$\frac{-7x}{-7}=\frac{-4}{-7}$

Simplify

$x=\frac{4}{7}$

Therefore,

The value of x = 4/7