Question

1. \\(\frac{r}{14}=\frac{2}{7}\\)\
2. \\(-26 = n - 12\\)\
3. \\(13v = -260\\)\
4. \\(-7 = n + 10\\)\
5. \\(m + 8 = 4\\)\
6. \\(-20 = 5n\\)\
7. \\(\frac{a}{10} = -5\\)\
8. \\(r - 5 = -2\\)

Explanation:

Let's solve each equation one by one:

Problem 11: $\boldsymbol{\frac{r}{14} = \frac{2}{7}}$

Step 1: Cross - multiply

To solve for $r$, we can cross - multiply. If $\frac{a}{b}=\frac{c}{d}$, then $a\times d = b\times c$. So for $\frac{r}{14}=\frac{2}{7}$, we have $r\times7=14\times2$.
$7r = 28$

Step 2: Solve for r

Divide both sides of the equation by 7: $r=\frac{28}{7}=4$

Step 1: Isolate n

To solve for $n$, we add 12 to both sides of the equation.
$n=-26 + 12$

Step 2: Calculate the value

$-26+12=-14$

Step 1: Solve for v

Divide both sides of the equation by 13.
$v=\frac{-260}{13}$

Step 2: Calculate the value

$\frac{-260}{13}=-20$

Answer:

$r = 4$

Problem 12: $\boldsymbol{-26=n - 12}$ (assuming the equation is $-26=n - 12$, since the original is a bit unclear, but following the pattern)