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

Step 1: Property to get Step 2: Property to get Step 3: Property to get Step 4: Property to get

3 answers

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

Step 1: Distribute on the right side

Use the distributive property on the right side of the equation:
\(3(4x + 5) = 12x + 15\)
Thus, the equation becomes: \[ 2x - 5 = 12x + 15 \]

Step 2: Move all terms involving \(x\) to one side

To do this, subtract \(2x\) from both sides: \[ -5 = 12x - 2x + 15 \]
This simplifies to: \[ -5 = 10x + 15 \]

Step 3: Move the constant term to the other side

Subtract \(15\) from both sides: \[ -5 - 15 = 10x \]
This simplifies to: \[ -20 = 10x \]

Step 4: Solve for \(x\)

Divide both sides by \(10\): \[ x = \frac{-20}{10} \]
This simplifies to: \[ x = -2 \]

Thus, the ordered steps with their corresponding properties are:

  1. Step 1: Distributive Property to get: \(2x - 5 = 12x + 15\)
  2. Step 2: Subtract \(2x\) from both sides to get: \(-5 = 10x + 15\)
  3. Step 3: Subtract \(15\) from both sides to get: \(-20 = 10x\)
  4. Step 4: Divide by \(10\) to get: \(x = -2\)
theres only 2x questions in the to get

Thank you for the clarification. Let's identify the steps again, this time focusing specifically on the intermediate equation forms involving \(2x\) only in the descriptions of the results:

Step 1: Distribute on the right side

Property: Distributive Property
Result: \(2x - 5 = 12x + 15\)

Step 2: Move all terms involving \(x\) to one side

Property: Subtract \(12x\) from both sides
Result: \(2x - 12x - 5 = 15\) or \(-10x - 5 = 15\)

Step 3: Move the constant term to the other side

Property: Add \(5\) to both sides
Result: \(-10x = 20\)

Step 4: Solve for \(x\)

Property: Divide by \(-10\)
Result: \(x = -2\)

The final ordered steps with descriptions about getting to each result are:

  1. Step 1: Distributive Property to get: \(2x - 5 = 12x + 15\)
  2. Step 2: Subtract \(12x\) from both sides to get: \(-10x - 5 = 15\)
  3. Step 3: Add \(5\) to both sides to get: \(-10x = 20\)
  4. Step 4: Divide by \(-10\) to get: \(x = -2\)

Let me know if this meets your expectations or if you need further adjustments!