Question

1)1-x/x+5=5/7 2)5/6 x +16=4x/9+9

Answer 1

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Answer 2

Let's solve the equations one by one:

1. $1 - \frac{x}{x + 5} = \frac{5}{7}$

To begin, let's get rid of the fractions by multiplying both sides of the equation by $7(x + 5)$:

$7(x + 5) - 7x = 5(x + 5)$

Expanding and simplifying:

$7x + 35 - 7x = 5x + 25$

The $7x$ and $-7x$ terms cancel out, leaving us with:

$35 = 5x + 25$

Subtracting 25 from both sides:

$35 - 25 = 5x$

$10 = 5x$

Finally, dividing both sides by 5:

$x = \frac{10}{5}$

$x = 2$

Therefore, the solution to the first equation is $x = 2$.

2. $\frac{5}{6}x + 16 = \frac{4x}{9} + 9$

To simplify the equation, let's eliminate the fractions by multiplying both sides by the least common multiple (LCM) of the denominators, which is 54:

$54 \left(\frac{5}{6}x + 16\right) = 54 \left(\frac{4x}{9} + 9\right)$

Expanding and simplifying:

$9(5x) + 54(16) = 6(4x) + 54(9)$

$45x + 864 = 24x + 486$

Moving all the $x$ terms to one side and the constant terms to the other side:

$45x - 24x = 486 - 864$

$21x = -378$

Dividing both sides by 21:

$x = \frac{-378}{21}$

$x = -18$

So, the solution to the second equation is $x = -18$.

To summarize:

1. $x = 2$
2. $x = -18$