To solve the equation \( 2x - 5 = 3(4x + 5) \), we can break the process into clear steps. Here’s the ordered sequence of steps to follow, along with the properties used:
Step 1: Distribute on the right-hand side.
\[ 2x - 5 = 3(4x + 5) \implies 2x - 5 = 12x + 15 \]
Property used: Distributive Property
Step 2: Move the terms involving \( x \) to one side of the equation.
\[ 2x - 12x = 15 + 5 \]
This simplifies to:
\[ -10x = 20 \]
Property used: Addition Property of Equality (adding \( 12x \) to both sides and adding 5 to both sides)
Step 3: Isolate \( x \) by dividing both sides by -10.
\[ x = \frac{20}{-10} \]
This simplifies to:
\[ x = -2 \]
Property used: Division Property of Equality
Step 4: Write the final answer.
\[ x = -2 \]
Property used: Solution conclusion
So, the ordered steps are:
- Distribute on the right-hand side.
- Move terms involving \( x \) to one side of the equation.
- Isolate \( x \) by division.
- Write the final answer.