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

Question

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) _____________
Fill In The Blanks
Options: Subtraction Property of Equality, x = 24, x = - 21/2, Division Property of Equality, 2x + 18 = -3, Addition Property of Equality, x = -9, 2x - 3 + 21 = -3, 2x = -21, 2x + 15 = -3, 2x = -18, -1x = -24, 2x - 6 + 21 = -3, Multiplication Property of Equality

Answer 1

Let's solve the equation step by step, filling in the blanks.

1. Distribute to get:
   \( 2(x - 3) + 21 = -3 \)
   Distributing gives:
   \( 2x - 6 + 21 = -3 \)

2. Combine like terms to get:
   Combining \(-6\) and \(21\) gives:
   \( 2x + 15 = -3 \)

3. Use the (choose a property):
   We will use the Subtraction Property of Equality to isolate \(2x\):
   Subtract \(15\) from both sides:
   \( 2x + 15 - 15 = -3 - 15 \)
   Resulting equation:
   \( 2x = -18 \)

4. Use the (choose a property):
   Now we will use the Division Property of Equality to solve for \(x\):
   Divide both sides by \(2\):
   \( x = \frac{-18}{2} \)
   Resulting answer:
   \( x = -9 \)

So, the completed solution is:

1. Distribute to get 2x - 6 + 21 = -3
2. Combine like terms to get 2x + 15 = -3
3. Use the (choose a property) Subtraction Property of Equality to get (resulting equation) 2x = -18
4. Use the (choose a property) Division Property of Equality to get (resulting answer) x = -9.

Answer 2

are you sure these answers are correct

Answer 3

Yes, let's verify the solution step by step to ensure everything is correct.

The original equation is:

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

1. Distribute to get:
   We need to distribute \(2\) into \((x - 3)\): \[ 2 \cdot x - 2 \cdot 3 + 21 = -3 \] This simplifies to: \[ 2x - 6 + 21 = -3 \]

2. Combine like terms to get:
   Combine the constants \(-6\) and \(21\): \[ 2x + 15 = -3 \]

3. Use the (choose a property):
   To isolate \(2x\), we will use the Subtraction Property of Equality. Subtract \(15\) from both sides: \[ 2x + 15 - 15 = -3 - 15 \] Resulting in: \[ 2x = -18 \]

4. Use the (choose a property):
   To solve for \(x\), we will use the Division Property of Equality. Divide both sides by \(2\): \[ x = \frac{-18}{2} \] Which simplifies to: \[ x = -9 \]

So, the final answer is indeed correct: \( x = -9 \).

To summarize:

1. Distribute to get 2x - 6 + 21 = -3
2. Combine like terms to get 2x + 15 = -3
3. Use the (choose a property) Subtraction Property of Equality to get (resulting equation) 2x = -18
4. Use the (choose a property) Division Property of Equality to get (resulting answer) x = -9.

These steps and answers are verified to be accurate.