Find the root of the equation 2 divided by (x + 10) equals negative 5.

Step-by-step solution

1. 1

   Record the excluded value first. The denominator may not be zero, so

   $x+10\neq 0\ \Longrightarrow\ x\neq -10$

   Writing this down before solving is what lets you spot an extraneous root at the end instead of reporting it.

2. 2

   Clear the denominator. Multiply both sides by $x+10$, which is legitimate precisely because we have excluded the value that makes it zero:

   $2=-5(x+10)$

3. 3

   Expand and isolate $x$.

   $2=-5x-50$

   $5x=-50-2$

   $5x=-52$

   $x=-\frac{52}{5}=-10.4$

4. 4

   Test the root against the exclusion. Is $-\tfrac{52}{5}=-10.4$ equal to $-10$? No — so the denominator is safe:

   $x+10=-10.4+10=-0.4\neq 0$

5. 5

   Substitute to verify the original equation.

   $\frac{2}{-0.4}=-5\quad\checkmark$

   The answer is exact: $x=-\dfrac{52}{5}$. A quick sanity check on the sign — the right side is negative, so $x+10$ had to be negative, which places $x$ just below $-10$, exactly where the root landed.