Solve the equation filling in the steps: 2(x−3)+21=−3

Distribute to get ____________________

Combine like terms to get ____________________

Use the (choose a property) ____________________ to get (resulting equation) ____________________

Use the (choose a property) ____________________ to get (resulting answer) ____________________

1 answer

Let's solve the equation step by step. The given equation is:

\[ 2(x - 3) + 21 = -3 \]

Step 1: Distribute to get

Distributing \( 2 \) inside the parentheses:

\[ 2(x) - 2(3) + 21 = -3 \]

This simplifies to:

\[ 2x - 6 + 21 = -3 \]

So, the answer is:

Distribute to get \( 2x - 6 + 21 = -3 \).


Step 2: Combine like terms to get

Now, we combine the like terms \(-6\) and \(21\):

\[ 2x + ( -6 + 21 ) = -3 \]

This simplifies to:

\[ 2x + 15 = -3 \]

So, the answer is:

Combine like terms to get \( 2x + 15 = -3 \).


Step 3: Use the (choose a property) to get (resulting equation)

Next, we want to isolate the term with \( x \) by using the addition property of equality. We subtract \( 15 \) from both sides:

\[ 2x + 15 - 15 = -3 - 15 \]

This results in:

\[ 2x = -18 \]

So, the answer is:

Use the addition property of equality to get \( 2x = -18 \).


Step 4: Use the (choose a property) to get (resulting answer)

Finally, we need to solve for \( x \) using the multiplication property of equality by dividing both sides by \( 2 \):

\[ \frac{2x}{2} = \frac{-18}{2} \]

This simplifies to:

\[ x = -9 \]

So, the answer is:

Use the multiplication property of equality to get \( x = -9 \).

In summary, we have:

  1. Distribute to get \( 2x - 6 + 21 = -3 \).
  2. Combine like terms to get \( 2x + 15 = -3 \).
  3. Use the addition property of equality to get \( 2x = -18 \).
  4. Use the multiplication property of equality to get \( x = -9 \).