Order the steps for solving the equation: 2x−5=3(4x+5) (8 points)

Answer 1

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

1. Distribute on the right side: Expand the expression on the right side of the equation. \[ 3(4x + 5) = 12x + 15 \] So, the equation becomes: \[ 2x - 5 = 12x + 15 \]

2. Move the terms involving \(x\) to one side: Subtract \(2x\) from both sides to isolate the \(x\) terms on one side. \[ -5 = 12x - 2x + 15 \] This simplifies to: \[ -5 = 10x + 15 \]

3. Isolate the \(x\) term: Subtract \(15\) from both sides of the equation. \[ -5 - 15 = 10x \] Simplifying gives: \[ -20 = 10x \]

4. Solve for \(x\): Divide both sides by \(10\) to solve for \(x\). \[ x = -2 \]

5. Check the solution: Substitute \(x = -2\) back into the original equation to verify the solution is correct. \[ 2(-2) - 5 = 3(4(-2) + 5) \] This simplifies to: \[ -4 - 5 = 3(-8 + 5) \] \[ -9 = 3(-3) \] \[ -9 = -9 \] The solution verifies correctly.

So, the correct order of steps to solve the equation \( 2x - 5 = 3(4x + 5) \) is:

1. Distribute on the right side.
2. Move the terms involving \(x\) to one side.
3. Isolate the \(x\) term.
4. Solve for \(x\).
5. Check the solution.

Answer 2

whats step 4 answer

Answer 3

In Step 4, when you divide both sides by 10 to solve for \(x\), you get:

\[ -20 = 10x \]

Dividing both sides by 10 gives:

\[ x = \frac{-20}{10} \]

So the answer for Step 4 is:

\[ x = -2 \]

This is the final solution to the equation \(2x - 5 = 3(4x + 5)\).