To solve the equation \(2x - 5 = 3(4x + 5)\), let's outline the steps in order and fill in the necessary information.
**Step 1: Distributive Property**
Start by applying the distributive property on the right side of the equation:
\[
2x - 5 = 3(4x + 5)
\]
This becomes:
\[
2x - 5 = 12x + 15
\]
**Step 2: Combine Like Terms**
Next, we want to get all the terms involving \(x\) on one side and constant terms on the other. We can subtract \(12x\) from both sides:
\[
2x - 12x - 5 = 15
\]
This simplifies to:
\[
-10x - 5 = 15
\]
**Step 3: Isolate the Variable**
Now, add \(5\) to both sides to isolate the term with \(x\):
\[
-10x = 15 + 5
\]
This simplifies to:
\[
-10x = 20
\]
**Step 4: Solve for the Variable**
Finally, divide by \(-10\) to solve for \(x\):
\[
x = \frac{20}{-10}
\]
This gives:
\[
x = -2
\]
So to summarize, here are the ordered steps for solving the equation:
1. **Distributive Property**: Expand the equation to get \(2x - 5 = 12x + 15\).
2. **Combine Like Terms**: Rearrange the equation to get \(-10x - 5 = 15\).
3. **Isolate the Variable**: Add \(5\) to both sides to obtain \(-10x = 20\).
4. **Solve for the Variable**: Divide by \(-10\) to find \(x = -2\).