Question

1. $-\frac{1}{2}=\frac{x}{10}$
2. $-42 = 7n$
3. $-11x = 209$
4. $2r + 7r=-8 + 7r$
5. $3b - 14 = 7b + 6$

Explanation:

Let's solve each equation one by one:

Equation 2: $-\frac{1}{2}=\frac{x}{10}$

Step 1: Cross - multiply to solve for $x$

We know that if $\frac{a}{b}=\frac{c}{d}$, then $a\times d = b\times c$. Here, $a = - 1$, $b = 2$, $c=x$, $d = 10$. So we have $-1\times10=2\times x$.
$$- 10 = 2x$$

Step 2: Divide both sides by 2

To isolate $x$, divide both sides of the equation $-10 = 2x$ by 2.
$$x=\frac{-10}{2}=-5$$

Step 1: Divide both sides by 7

To solve for $n$, divide both sides of the equation $-42=7n$ by 7.
$$n=\frac{-42}{7}=-6$$

Step 1: Divide both sides by - 11

To isolate $x$, divide both sides of the equation $-11x = 209$ by $-11$.
$$x=\frac{209}{-11}=-19$$

Answer:

$x = - 5$

Equation 4: $-42 = 7n$