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




(8 points)
2x−5=3(4x+5)
Step 1:
Combine Like Terms
Property to get


Step 2:
Distributive
Property to get

Step 3:
Division of Equality
Property to get

Step 4:
Addition of Equality
Property to get

1 answer

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

Step 1: Distributive Property to get

Use the distributive property to expand the right side of the equation: \[ 2x - 5 = 3 \cdot 4x + 3 \cdot 5 \quad \Rightarrow \quad 2x - 5 = 12x + 15 \]

Step 2: Addition of Equality Property to get

Add 5 to both sides of the equation to isolate the terms involving \( x \): \[ 2x - 5 + 5 = 12x + 15 + 5 \quad \Rightarrow \quad 2x = 12x + 20 \]

Step 3: Combine Like Terms Property to get

Subtract \( 12x \) from both sides of the equation: \[ 2x - 12x = 20 \quad \Rightarrow \quad -10x = 20 \]

Step 4: Division of Equality Property to get

Divide both sides by -10 to solve for \( x \): \[ x = \frac{20}{-10} \quad \Rightarrow \quad x = -2 \]

So, the ordered steps for solving the equation are:

  1. Step 1: Distributive Property to get \( 2x - 5 = 12x + 15 \)
  2. Step 2: Addition of Equality Property to get \( 2x = 12x + 20 \)
  3. Step 3: Combine Like Terms Property to get \( -10x = 20 \)
  4. Step 4: Division of Equality Property to get \( x = -2 \)

This is the correct order of steps to solve the equation.