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

4 solving steps and 4 property's used

1 answer

To solve the equation \( 7(x + 4) = 5(x + 2) \) using four solving steps and identifying the properties used, follow these steps:

Step 1: Distribute

Property Used: Distributive Property \[ 7(x + 4) = 7x + 28 \quad \text{and} \quad 5(x + 2) = 5x + 10 \] This rewrites the equation as: \[ 7x + 28 = 5x + 10 \]

Step 2: Subtract \(5x\) from both sides

Property Used: Subtraction Property of Equality \[ 7x + 28 - 5x = 5x + 10 - 5x \] This simplifies to: \[ 2x + 28 = 10 \]

Step 3: Subtract 28 from both sides

Property Used: Subtraction Property of Equality \[ 2x + 28 - 28 = 10 - 28 \] Now, we have: \[ 2x = -18 \]

Step 4: Divide both sides by 2

Property Used: Division Property of Equality \[ \frac{2x}{2} = \frac{-18}{2} \] This gives: \[ x = -9 \]

Summary:

  1. Distributive Property: \( 7(x + 4) = 5(x + 2) \) transforms to \( 7x + 28 = 5x + 10 \)
  2. Subtraction Property of Equality: Subtracting \(5x\) leads to \(2x + 28 = 10\)
  3. Subtraction Property of Equality: Subtracting 28 leads to \(2x = -18\)
  4. Division Property of Equality: Dividing by 2 gives \(x = -9\)

So, the solution to the equation is \( x = -9 \).