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
2x - 5 = 12x + 5


Step 2:
Addition of Equality
Property to get
2x = 12x + 10

Step 3:
Distributive
Property to get
-1x = 10

Step 4:
Division of Equality
Property to get
x = -1/10

Answer 1

Subtraction of Similar Terms is not an option

Answer 2

To correctly solve the equation \( 2x - 5 = 3(4x + 5) \) and order the steps accordingly, let's review the correct sequence of operations and clarify the terminology used.

1. Start with the original equation:
\[
2x - 5 = 3(4x + 5)
\]

2. **Step 1: Distributive Property**
Apply the distributive property on the right side:
\[
2x - 5 = 12x + 15
\]

3. **Step 2: Addition of Equality Property**
Add 5 to both sides to isolate terms involving \(x\):
\[
2x = 12x + 20
\]

4. **Step 3: Subtraction of Similar Terms**
Subtract \(12x\) from both sides:
\[
2x - 12x = 20
\]
\[
-10x = 20
\]

5. **Step 4: Division of Equality Property**
Divide both sides by -10:
\[
x = -\frac{20}{10} = -2
\]

So the ordered steps to correctly solve the equation \( 2x - 5 = 3(4x + 5) \) are:

1. **Distributive Property**: \( 2x - 5 = 12x + 15 \)
2. **Addition of Equality Property**: \( 2x = 12x + 20 \)
3. **Subtraction of Similar Terms**: \( -10x = 20 \)
4. **Division of Equality Property**: \( x = -2 \)

(Note: The steps you provided had some errors and need adjusting for both the operations and the results.)

Answer 3

Thank you for your clarification! Let's reorder the steps using only the operations you've provided. Based on your original question, here’s a correction to ensure we follow the stated framework:

Given:
\( 2x - 5 = 3(4x + 5) \)

### Correct Steps to Solve:

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

2. **Step 2: Addition of Equality Property**
Rearrange to isolate terms involving \(x\). You effectively need to move \(12x\) to the left side; however, using only the addition property we have:
\[
2x - 12x = 15 + 5
\]
(This can be seen as adding \(-12x\) and \(5\) to both sides):
\[
-10x = 20
\]

3. **Step 3: Division of Equality Property**
Divide both sides by \(-10\):
\[
x = -\frac{20}{10} = -2
\]

Based on the options provided in your original message, here's the structured approach:

1. **Distributive Property**: \( 2x - 5 = 12x + 15 \) (Step 1)
2. **Addition of Equality Property**: Rearranged to \( -10x = 20 \) (Step 2 - implicit step)
3. **Division of Equality Property**: \( x = -2 \) (Step 4)

An important note is that if "Subtraction of Similar Terms" isn’t an option, we can realize rearrangement can be achieved through addition. Thank you for your understanding, and I hope this accurately reflects the steps you can proceed with!