1. Let's start by stating the problem: Solve the inequality $$-5(u - 19) \leq -11 + 2u$$. 2. Begin by distributing the -5 on the left side: $$-5 \cdot u + (-5) \cdot (-19) \leq -11 + 2u$$ which simplifies to $$-5u + 95 \leq -11 + 2u$$. 3. Next, collect like terms by adding $$5u$$ to both sides: $$95 \leq -11 + 2u + 5u$$ which is $$95 \leq -11 + 7u$$. 4. Then add 11 to both sides to isolate the term with $$u$$: $$95 + 11 \leq 7u$$ so $$106 \leq 7u$$. 5. Finally, divide both sides by 7 to solve for $$u$$: $$\frac{106}{7} \leq u$$ or equivalently $$u \geq \frac{106}{7}$$. 6. Simplify the fraction to a mixed number or decimal if desired: $$\frac{106}{7} = 15\frac{1}{7} \approx 15.14$$. 7. Thus, the solution is all $$u$$ such that $$u \geq \frac{106}{7}$$. 8. The number line in the problem shows a shaded region from -19 to -11, but based on the algebra, the solution is $$u \geq 15.14$$, beyond 13, so the shaded region seems inconsistent with the inequality solution. The correct solution is the interval $$[\frac{106}{7}, \infty)$$.