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

Question

(8 points)
2x−5=3(4x+5)
Step 1:
Distributive
Property to get
2x - 5 = 12x + 5


Step 2:
Combine Like Terms
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:

1. Step 1: Distributive Property \[ 2x - 5 = 3(4x + 5) \implies 2x - 5 = 12x + 15 \]

2. Step 2: Combine Like Terms To get all the \( x \) terms on one side and constant terms on the other side, we can rearrange the equation: \[ 2x - 12x = 15 + 5 \implies -10x = 20 \]

3. Step 3: Solve for x Now, divide both sides by -10: \[ x = \frac{20}{-10} \implies x = -2 \]

4. Step 4: Check the Solution Substitute \( x = -2 \) back into the original equation to ensure it holds: \[ 2(-2) - 5 = 3(4(-2) + 5) \implies -4 - 5 = 3(-8 + 5) \implies -9 = 3(-3) \implies -9 = -9 \] The equation is satisfied.

So the ordered steps are:

1. Distributive Property to get: \( 2x - 5 = 12x + 15 \)
2. Combine Like Terms to get: \( -10x = 20 \)
3. Solve for \( x \) to get: \( x = -2 \)
4. Check the solution to verify the result.