Question

Question

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



(8 points)
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

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Answer 1

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

1. Step 1: Distribute on the right side of the equation. \[ 2x - 5 = 12x + 15 \] (This involves applying the distributive property: \( 3(4x + 5) = 3 \cdot 4x + 3 \cdot 5 = 12x + 15 \))

2. Step 2: Subtract \( 12x \) from both sides. \[ 2x - 12x - 5 = 15 \] (This involves combining like terms to isolate \( x \) on one side)

3. Step 3: Combine like terms. \[ -10x - 5 = 15 \]

4. Step 4: Add 5 to both sides. \[ -10x = 20 \]

5. Step 5: Divide by -10. \[ x = -2 \]

So the completed ordered steps for the equation \( 2x - 5 = 3(4x + 5) \) are:

• Step 1: Distribute on the right side of the equation.
• Step 2: Subtract \( 12x \) from both sides.
• Step 3: Combine like terms on the left side.
• Step 4: Add 5 to both sides.
• Step 5: Divide by -10 to solve for \( x \).

Your output should reflect the step-wise approach to arriving at the solution.

Answer 2

do it more clearly

Answer 3

Sure! Let's clearly outline the steps to solve the equation \( 2x - 5 = 3(4x + 5) \) in a more structured way:

Solve the Equation \( 2x - 5 = 3(4x + 5) \)

Step 1: Distribute

• Apply the distributive property to the right side of the equation.
• Rewrite the equation: \[ 2x - 5 = 3 \cdot 4x + 3 \cdot 5 \] This results in: \[ 2x - 5 = 12x + 15 \]

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

• Subtract \( 12x \) from both sides: \[ 2x - 12x - 5 = 15 \] This simplifies to: \[ -10x - 5 = 15 \]

Step 3: Move constant terms to the other side

• Add \( 5 \) to both sides: \[ -10x - 5 + 5 = 15 + 5 \] This simplifies to: \[ -10x = 20 \]

Step 4: Solve for \( x \)

• Divide both sides by -10: \[ x = \frac{20}{-10} \] Which simplifies to: \[ x = -2 \]

Final Solution:

The solution to the equation \( 2x - 5 = 3(4x + 5) \) is: \[ \boxed{x = -2} \]

This structured format clearly walks through each step in a logical sequence.