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

Question

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
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

#: 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 solve the equation step-by-step by filling in the necessary responses.

Given the equation:

\[ 2(x−3)+21=−3 \]

Step 1: Distribute

First, we need to distribute the \(2\) in the equation.

Distributing gives us: \[ 2x - 6 + 21 = -3 \]

So, the response is: Distribute to get: 2x - 6 + 21 = -3

Step 2: Combine like terms

Next, we combine like terms on the left side of the equation.

Combining \(-6 + 21\) gives us \(15\): \[ 2x + 15 = -3 \]

So, the response is: Combine like terms to get: 2x + 15 = -3

Step 3: Isolate the variable

To isolate \(x\), we'll use the Subtraction Property of Equality:

Subtract \(15\) from both sides: \[ 2x = -3 - 15 \]

Calculating gives us: \[ 2x = -18 \]

So, the response is: Use the (choose a property) response area to get: 2x = -18

Step 4: Solve for x

Now, we can solve for \(x\) using the Division Property of Equality:

Divide both sides by \(2\): \[ x = \frac{-18}{2} \]

Calculating gives us: \[ x = -9 \]

So, the response is: Use the (choose a property) response area to get: x = -9

Summary of results:

The final result of the equation is: \[ x = -9 \]