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Order the steps for solving the equation:

2x − 5 = 3 (4x + 5)
Your options are:
Combine Like Terms
Distrubitive property
Addition of equality
Subtraction of equality
Division of equality

1 answer

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

  1. Distributive property: Apply the distributive property to the right side of the equation. \[ 2x - 5 = 12x + 15 \]

  2. Addition of equality: Add 5 to both sides to eliminate the -5 on the left side. \[ 2x = 12x + 20 \]

  3. Subtraction of equality: Subtract \(12x\) from both sides to move the \(x\) terms on one side. \[ -10x = 20 \]

  4. Division of equality: Divide both sides by -10 to solve for \(x\). \[ x = -2 \]

  5. Combine Like Terms: (This step is not specifically needed in this context because the terms are already grouped properly during the subtraction step; however, it might be considered at earlier stages if simplifying).

So, the correct order of steps to follow is:

  1. Distributive property
  2. Addition of equality
  3. Subtraction of equality
  4. Division of equality

Combining like terms is intrinsic within these steps but doesn't require a separate step in this instance.