Question

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

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Answer 1

put them all together in a sentence

Answer 2

To solve the equation \( 2(x - 3) + 21 = -3 \), we can break down the solution into clear steps.

1. **Distribute**:
We will distribute the \(2\) in the equation.

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

So, the equation becomes:

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

2. **Combine like terms**:
Next, we can combine the constants \(-6\) and \(21\).

\[
-6 + 21 = 15
\]

So, the equation now is:

\[
2x + 15 = -3
\]

3. **Use the subtraction property of equality**:
We will subtract \(15\) from both sides of the equation to isolate the term with \(x\).

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

Which simplifies to:

\[
2x = -18
\]

4. **Use the division property of equality**:
Now, we divide by \(2\) to solve for \(x\).

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

This gives us:

\[
x = -9
\]

So, the final solution is

\[
\boxed{-9}
\]

Answer 3

To solve the equation \(2(x - 3) + 21 = -3\), first, distribute to obtain \(2x - 6 + 21 = -3\); then, combine like terms to get \(2x + 15 = -3\); next, use the subtraction property of equality to isolate the variable, resulting in \(2x = -18\); finally, apply the division property of equality to find that \(x = -9\).