Question

Order the steps for solving the equation: 2x−5=3(4x+5)


(8 points)
2x−5=3(4x+5)
Step 1:
Distributive
Property to get
2x - 5 = 12x + 15


Step 2:
Addition of Equality
Property to get
2x = 3x + 10

Step 3:
Combine Like Terms
Property to get
-10x = 20

Step 4:
Division of Equality
Property to get
x = -2

Answer 1

To solve the equation \(2x - 5 = 3(4x + 5)\), we can follow these steps in the correct order:

1. **Step 1: Distributive Property** to get:
\[
2x - 5 = 12x + 15
\]

2. **Step 2: Addition of Equality Property** to get:
\[
2x - 12x = 15 + 5 \quad \text{(adding -12x to both sides and } +5 \text{ to both sides)}
\]
This simplifies to:
\[
-10x = 20
\]

3. **Step 3: Division of Equality Property** to get:
\[
x = -2 \quad \text{(dividing both sides by -10)}
\]

Note that the step where you mentioned "Combine Like Terms" isn't necessary in that way, since once \(2x - 12x = 20\) is simplified directly.

So the correct order of steps should be:

1. **Step 1: Distributive Property**
2. **Step 2: Addition of Equality Property**
3. **Step 3: Combine Like Terms (which occurs in Step 2) but is implied**
4. **Step 4: Division of Equality Property**

Final ordered steps:

1. Distributive Property to get \(2x - 5 = 12x + 15\)
2. Addition of Equality Property to get \(-10x = 20\)
3. Division of Equality Property to get \(x = -2\)