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7(x+4) = 5(x+2)

give me 4 of the solving steps and 4 of the property used

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Let's solve the equation \( 7(x+4) = 5(x+2) \) step by step and identify the properties used.

Solving Steps:

  1. Distribute the Terms: \[ 7(x+4) = 7x + 28 \quad \text{and} \quad 5(x+2) = 5x + 10 \] So, the equation becomes: \[ 7x + 28 = 5x + 10 \]

  2. Isolate the Variable: Subtract \( 5x \) from both sides: \[ 7x - 5x + 28 = 10 \] Simplifying this gives: \[ 2x + 28 = 10 \]

  3. Move the Constant: Subtract 28 from both sides: \[ 2x + 28 - 28 = 10 - 28 \] This simplifies to: \[ 2x = -18 \]

  4. Solve for \( x \): Divide both sides by 2: \[ x = \frac{-18}{2} = -9 \]

Properties Used:

  1. Distributive Property: Used to expand \( 7(x+4) \) and \( 5(x+2) \) to \( 7x + 28 \) and \( 5x + 10 \), respectively.

  2. Subtraction Property of Equality: Used when subtracting \( 5x \) from both sides and when subtracting 28 from both sides to maintain equality.

  3. Addition Property of Equality: (Not directly used in these steps, but often required when you would add a term to both sides to isolate a variable, as shown when moving constants.)

  4. Division Property of Equality: Used when dividing both sides by 2 to solve for \( x \).

Thus, by following these steps and applying these properties, we found that \( x = -9 \).