1. The problem is to find three different equations that have the same solution as the equation $2x + 9 = -15$. 2. First, solve the original equation to find the solution for $x$. 3. Start by isolating $x$: $$2x + 9 = -15$$ Subtract 9 from both sides: $$2x + \cancel{9} - \cancel{9} = -15 - 9$$ $$2x = -24$$ 4. Divide both sides by 2 to solve for $x$: $$\frac{2x}{\cancel{2}} = \frac{-24}{\cancel{2}}$$ $$x = -12$$ 5. Now, create three different equations that have the same solution $x = -12$. Equation 1: Multiply the original equation by 3: $$3(2x + 9) = 3(-15)$$ $$6x + 27 = -45$$ Equation 2: Add 5 to both sides of the original equation and then subtract 5 from both sides: $$2x + 9 + 5 = -15 + 5$$ $$2x + 14 = -10$$ Equation 3: Subtract 4 from both sides and then add 4 to both sides: $$2x + 9 - 4 = -15 - 4$$ $$2x + 5 = -19$$ 6. Each of these equations has the same solution $x = -12$ because they are derived by performing equivalent operations on the original equation, which do not change the solution. Final answer: - $6x + 27 = -45$ - $2x + 14 = -10$ - $2x + 5 = -19$