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

(6 points)
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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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3 answers

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

\[ \boxed{-9} \]

put them all together in a sentence

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 \(x = -9\).