1. **State the problem:** Solve the inequality $-2(5v - 12) > 6 - v$ and verify the solution $v \leq 2$. 2. **Distribute the $-2$ on the left side:** $$-2 \times 5v = -10v, \quad -2 \times (-12) = +24$$ So the inequality becomes: $$-10v + 24 > 6 - v$$ 3. **Bring all terms involving $v$ to one side and constants to the other:** Add $10v$ to both sides: $$\cancel{-10v} + 24 > 6 - v + 10v$$ $$24 > 6 + 9v$$ 4. **Subtract 6 from both sides:** $$24 - 6 > 6 - 6 + 9v$$ $$18 > 9v$$ 5. **Divide both sides by 9 to isolate $v$:** $$\frac{18}{\cancel{9}} > \frac{9v}{\cancel{9}}$$ $$2 > v$$ 6. **Rewrite the inequality in standard form:** $$v < 2$$ 7. **Compare with the given solution $v \leq 2$:** Our solution is $v < 2$, which is slightly stricter than $v \leq 2$. **Final answer:** $$v < 2$$