Solve the equation filling in the steps: 2(x−3)+21=−3(6 points)

Question

Distribute to get Response area

Combine like terms to get Response area

Use the (choose a property) Response area to get (resulting equation) Response area

Use the (choose a property) Response area to get (resulting answer) Response area

# x =24

# x = - 21/2

#: 2x =- 18

:: Subtraction Property of Equality

# 2x-6+21 =- 3

:: 2x+15 =- 3

# 2x-3+21 =- 3

# x =- 21

#: Multiplication Property of Equality

#: 2x+18 =- 3

:: 2x =- 21

#-1x =- 24

# Division Property of Equality

# Addition Property of Equality

# =- 9

Answer 1

Let's carefully solve the equation step by step, including distribution, combining like terms, and applying relevant properties.

Given equation:

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

Step 1: Distribute

Distributing the \(2\) to both terms inside the parentheses: \[ 2(x) - 2(3) + 21 = -3 \] This gives: \[ 2x - 6 + 21 = -3 \]

Step 2: Combine like terms

Now combine \( -6 \) and \( 21 \): \[ 2x + 15 = -3 \]

Step 3: Use the Subtraction Property of Equality

To isolate the term with \( x \), subtract \( 15 \) from both sides: \[ 2x + 15 - 15 = -3 - 15 \] This simplifies to: \[ 2x = -18 \]

Step 4: Use the Division Property of Equality

Next, divide both sides by \( 2 \): \[ \frac{2x}{2} = \frac{-18}{2} \] This simplifies to: \[ x = -9 \]

Final Answer:

\[ x = -9 \]

Thus, the final solution we have found is \( x = -9 \).

Summary of Responses:

1. Distribute to get: 2x - 6 + 21 = -3
2. Combine like terms to get: 2x + 15 = -3
3. Use the Subtraction Property of Equality to get: 2x = -18
4. Use the Division Property of Equality to get: x = -9