Solve the equation -2x - 9 = -15.

Step-by-step solution

1. 1

   Undo the addition before the multiplication. The expression $-2x-9$ was built by multiplying $x$ by $-2$ and then subtracting $9$, so unwinding it reverses that order: deal with the $-9$ first. Add $9$ to both sides:

   $-2x-9+9=-15+9\qquad\Longrightarrow\qquad-2x=-6$

   On the right, $-15+9=-6$: adding a positive to a negative moves toward zero.

2. 2

   Divide both sides by the coefficient $-2$.

   $\frac{-2x}{-2}=\frac{-6}{-2}\qquad\Longrightarrow\qquad x=3$

   A negative divided by a negative is positive, so the answer is $+3$, not $-3$. Dropping one of the two minus signs is the most common failure here.

3. 3

   Verify in the original equation. Substitute $x=3$:

   $-2(3)-9=-6-9=-15\ \checkmark$

   The left side matches the right side exactly, so $x=3$ is the solution.

4. 4

   Note the alternative route. Multiplying the whole equation by $-1$ first gives $2x+9=15$, then $2x=6$ and $x=3$ ✓ — the same answer with all-positive arithmetic. Clearing the negative coefficient up front is often the safer habit when several negatives appear.

5. 5

   Check uniqueness. The equation is linear with a non-zero coefficient of $x$, so its graph is a straight line of slope $-2$ crossing the horizontal line $y=-15$ exactly once. There is therefore precisely one solution — no need to look for others.