After combining like terms to simplify the equation

Question

3 - 15x + 24 + 16x = 4x - 24 - 4x, what would be the next best step to finish solving?
A. Subtract 24 from both sides of the equation.
B. Add x to both sides of the equation.
C. Subtract 27 from both sides of the equation.
D. Subtract x from both sides of the equation.
E. Divide both sides of the equation by 15.

Answer 1

Let's first simplify the given equation step by step:

Starting with: \[ 3 - 15x + 24 + 16x = 4x - 24 - 4x \]

Combine like terms on both sides: \[ (3 + 24) + (-15x + 16x) = (4x - 4x) - 24 \] \[ 27 + x = -24 \]

Now we have the simplified equation: \[ 27 + x = -24 \]

Next, to solve for \( x \), we need to isolate \( x \). The best step here is to eliminate the constant on the left side. Therefore, we can subtract 27 from both sides:

This leads us to: \[ x = -24 - 27 \]

So the correct next step to finish solving the equation is: C. Subtract 27 from both sides of the equation.

Answer 2

are you sure this is correct

Answer 3

Let’s go through the entire simplification and solving process step-by-step again to ensure accuracy.

Starting from the original equation: \[ 3 - 15x + 24 + 16x = 4x - 24 - 4x \]

1. Combine like terms on the left side:

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

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

2. Now simplify the right side:

   • The \(4x - 4x\) cancels out to \(0\)
   • So the right side is: \[ -24 \]

Now, the equation simplifies to: \[ 27 + x = -24 \]

To isolate \(x\), we subtract 27 from both sides: \[ x = -24 - 27 \]

This means the result is: \[ x = -51 \]

Thus, the next best step to finish solving from the simplified equation \(27 + x = -24\) was indeed to subtract 27 from both sides.

So the original step mentioned was correct; the answer is still: C. Subtract 27 from both sides of the equation.

Thank you for your patience! If you have any more questions or need further assistance, feel free to ask.