To solve the equation $2x - 5 = 3(4x + 5)$, we need to follow a logical sequence of steps. Let's analyze and order the steps correctly:

Given Equation

$2x - 5 = 3(4x + 5)$

Step 1: Distributive Property

• Apply the distributive property to the right-hand side of the equation. $2x - 5 = 12x + 15$

Step 2: Subtraction of Equality Property

• Subtract $12x$ from both sides to get the $x$ terms on one side. $2x - 12x - 5 = 12x - 12x + 15$ $-10x - 5 = 15$

Step 3: Addition of Equality Property

• Add 5 to both sides to isolate the $x$ term. $-10x - 5 + 5 = 15 + 5$ $-10x = 20$

Step 4: Division of Equality Property

• Divide both sides by $-10$ to solve for $x$. $x = \frac{20}{-10}$ $x = -2$

Correct Order of Steps:

1. Step 1: Distributive Property to get $2x - 5 = 12x + 15$.
2. Step 3: Subtraction of Equality Property to get $-10x - 5 = 15$.
3. Step 2: Addition of Equality Property to get $-10x = 20$.
4. Step 4: Division of Equality Property to get $x = -2$.

Would you like more details or have any questions? Here are some related questions to explore:

1. What would happen if we had $-3(4x + 5)$ instead of $3(4x + 5)$?
2. How can we verify the solution $x = -2$ is correct?
3. What methods can be used to solve similar equations with different coefficients?
4. How does changing the constant terms affect the solution?
5. Can these steps be applied to solve equations with fractions?

Tip: Always check your solution by substituting it back into the original equation to ensure it satisfies the equation.