Question

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



(8 points)
2x−5=3(4x+5)
Step 1:
Combine Like Terms
Property to get


Step 2:
Distributive
Property to get

Step 3:
Division of Equality
Property to get

Step 4:
Addition of Equality
Property to get

Answer 1

To solve the equation \( 2x - 5 = 3(4x + 5) \), the steps can be arranged as follows:

### Step 1: Distributive Property to get
Use the distributive property to expand the right side of the equation:
\[
2x - 5 = 3 \cdot 4x + 3 \cdot 5 \quad \Rightarrow \quad 2x - 5 = 12x + 15
\]

### Step 2: Addition of Equality Property to get
Add 5 to both sides of the equation to isolate the terms involving \( x \):
\[
2x - 5 + 5 = 12x + 15 + 5 \quad \Rightarrow \quad 2x = 12x + 20
\]

### Step 3: Combine Like Terms Property to get
Subtract \( 12x \) from both sides of the equation:
\[
2x - 12x = 20 \quad \Rightarrow \quad -10x = 20
\]

### Step 4: Division of Equality Property to get
Divide both sides by -10 to solve for \( x \):
\[
x = \frac{20}{-10} \quad \Rightarrow \quad x = -2
\]

So, the ordered steps for solving the equation are:

1. **Step 1:** Distributive Property to get \( 2x - 5 = 12x + 15 \)
2. **Step 2:** Addition of Equality Property to get \( 2x = 12x + 20 \)
3. **Step 3:** Combine Like Terms Property to get \( -10x = 20 \)
4. **Step 4:** Division of Equality Property to get \( x = -2 \)

This is the correct order of steps to solve the equation.