1. The first problem is to solve the equation $$7r + 2 \times 7r + 3 = -(7)(-2r)$$ for $r$. 2. First, simplify the left side by distributing and combining like terms. 3. The left side is $$7r + 2 \times 7r + 3 = 7r + 14r + 3 = 21r + 3$$. 4. The right side is $$-(7)(-2r) = 14r$$. 5. So the equation becomes $$21r + 3 = 14r$$. 6. Subtract $14r$ from both sides: $$21r + 3 - 14r = 14r - 14r$$ $$\cancel{21r} + 3 - \cancel{14r} = 0$$ $$7r + 3 = 0$$. 7. Subtract 3 from both sides: $$7r + 3 - 3 = 0 - 3$$ $$7r = -3$$. 8. Divide both sides by 7: $$\frac{7r}{\cancel{7}} = \frac{-3}{7}$$ $$r = -\frac{3}{7}$$. Final answer: The value of $r$ is $-\frac{3}{7}$.