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

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

9 answers

Let's solve the equation step by step:

  1. Original equation:

    \[ 2(x−3)+21=−3 \]

  2. Distribute to get:

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

    (Here, \(2\) is multiplied by both \(x\) and \(-3\).)

  3. Combine like terms to get:

    \[ 2x + 15 = -3 \]

    (The \(-6\) and \(21\) combine to \(15\).)

  4. Use the subtraction property of equality to get:

    \[ 2x = -3 - 15 \]

    (We subtract \(15\) from both sides of the equation.)

  5. Combine to get:

    \[ 2x = -18 \]

  6. Use the division property of equality to get:

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

    (We divide both sides by \(2\).)

  7. Simplify to get:

    \[ x = -9 \]

So, the solution to the equation is \(x = -9\).

To summarize:

  • Distribute to get: \(2x - 6 + 21 = -3\)
  • Combine like terms to get: \(2x + 15 = -3\)
  • Use the subtraction property of equality to get: \(2x = -3 - 15\)
  • Use the division property of equality to get: \(x = -9\)
I don't see that option for step 4, what is another way to say the 4th step?

Absolutely! For step 4, instead of saying "Use the subtraction property of equality," you can say:

Use the additive inverse property to get:

\[ 2x = -3 - 15 \]

The additive inverse property emphasizes that to isolate \(x\), we are effectively "removing" \(15\) from the left side by adding its opposite, which is \(-15\).

So, the revised step could be:

  1. Use the additive inverse property to get:

\[ 2x = -3 - 15 \]

Thank you for pointing that out!

I don't see 2x = -3 - 15

I apologize for the confusion in the explanation. Let's clarify and rewrite that step correctly.

After combining like terms, we had:

\[ 2x + 15 = -3 \]

When isolating \(2x\), you subtract \(15\) from both sides of the equation. Let's rewrite step 4 clearly and correctly:

  1. Use the additive inverse property to get:

\[ 2x = -3 - 15 \]

This is correct. Now combining the right-hand side:

\[ 2x = -18 \]

So indeed, after subtracting \(15\) from both sides, we correctly reach \(2x = -18\).

To summarize the steps one more time:

  1. Original equation: \[ 2(x−3)+21=−3 \]

  2. Distribute: \[ 2x - 6 + 21 = -3 \]

  3. Combine like terms: \[ 2x + 15 = -3 \]

  4. Use the additive inverse property to isolate \(2x\): \[ 2x = -3 - 15 \]

  5. Combine: \[ 2x = -18 \]

  6. Use the division property of equality: \[ x = \frac{-18}{2} \]

  7. Simplify: \[ x = -9 \]

Your final answer is \(x = -9\). Thank you for your patience, and I hope this clears up any confusion!

I mean for step 3, what is another way to say step 3?

For step 3, instead of saying "Combine like terms," you could say:

Simplify the left side to get:

This highlights the action of combining the constants directly without specifically labeling them as "like terms."

So, step 3 would then be rewritten as:

  1. Simplify the left side to get:

\[ 2x + 15 = -3 \]

Thank you for your feedback, and I'm glad to provide alternative phrasing!

That is step 2, not 3

I apologize for the mix-up. Let's clarify step 3 correctly. After you have distributed and simplified the left side in step 2, you have:

\[ 2x + 15 = -3 \]

Now for step 3, instead of saying "Combine like terms," you can say:

Move the constant to the right side to get:

\[ 2x = -3 - 15 \]

So the revised step 3 could be phrased as:

  1. Move the constant to the right side to get:

\[ 2x = -3 - 15 \]

Thank you for your patience as we clarify these steps!