1. **Stating the problem:** Find the value of $x$ from the equation: $$-2x \begin{bmatrix}-1 & 5\end{bmatrix} = 6$$ 2. **Understanding the equation:** The expression $-2x \begin{bmatrix}-1 & 5\end{bmatrix}$ represents scalar multiplication of the matrix by $-2x$. 3. **Rewrite the equation:** $$\begin{bmatrix}-2x \times (-1) & -2x \times 5\end{bmatrix} = \begin{bmatrix}6 & 6\end{bmatrix}$$ 4. **Simplify each element:** $$\begin{bmatrix}2x & -10x\end{bmatrix} = \begin{bmatrix}6 & 6\end{bmatrix}$$ 5. **Set up equations from corresponding elements:** 1) $2x = 6$ 2) $-10x = 6$ 6. **Solve the first equation:** $$2x = 6$$ $$x = \frac{6}{2}$$ $$x = 3$$ 7. **Solve the second equation:** $$-10x = 6$$ $$x = \frac{6}{-10}$$ $$x = -\frac{3}{5}$$ 8. **Check for consistency:** The two values of $x$ are different, so the equation as given cannot hold for both elements simultaneously unless the problem means something else or the matrix equality is misunderstood. 9. **Assuming the problem means the scalar product equals 6 (a scalar), not a matrix:** Then: $$-2x \times (-1) = 6$$ $$2x = 6$$ $$x = 3$$ 10. **Final answer:** $$\boxed{3}$$ This is the consistent solution for $x$ if the problem is interpreted as scalar multiplication of the first element only.