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

Question

(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

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 2

Subtraction of Similar Terms is not an option

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!