11. After combining like terms to simplify the equation 3−15x+24+16x=4x−24−4x

, what would be the next best step to finish solving?(1 point)
Responses

Add x to both sides of the equation.
Add x to both sides of the equation.

Subtract 24 from both sides of the equation.
Subtract 24 from both sides of the equation.

Subtract 27 from both sides of the equation.
Subtract 27 from both sides of the equation.

Divide both sides of the equation by 15.
Divide both sides of the equation by 15.

Subtract x from both sides of the equation.

1 answer

First, let's simplify the equation \( 3 - 15x + 24 + 16x = 4x - 24 - 4x \).

Combining like terms on the left side:

  • The constant terms: \( 3 + 24 = 27 \)
  • The x terms: \( -15x + 16x = 1x \) or just \( x \)

So, the left side simplifies to: \[ 27 + x \]

On the right side, combine like terms:

  • \( 4x - 4x = 0 \)
  • The constant is \( -24 \), so the right side simplifies to: \[ -24 \]

Now, the equation looks like this: \[ 27 + x = -24 \]

To isolate \( x \), the next best step would be to subtract 27 from both sides of the equation.

Therefore, the correct response is: Subtract 27 from both sides of the equation.