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 areaCombine like terms to get Response areaUse the (choose a property) Response area to get (resulting equation) Response areaUse the (choose a property) Response area to get (resulting answer) Response areaMultiplication Property of Equalityx=24Division Property of Equality2x+15=−32x−3+21=−32x=−18Subtraction Property of Equality2x+18=−3Addition Property of Equality−1x=−242x−6+21=−3x=−9x=−2122x=−21Skip to navigationPreviousNext

Answer 1

Let's solve the equation step by step, filling in the required responses for each part of the solution.

1. Distribute to get Response area: \[ 2(x−3)+21 = −3 \] Distributing the 2: \[ 2x - 6 + 21 = -3 \]

   Response area:
   \( 2x - 6 + 21 = -3 \)

2. Combine like terms to get Response area: Now combine \(-6\) and \(21\): \[ 2x + 15 = -3 \]

   Response area:
   \( 2x + 15 = -3 \)

3. Use the (choose a property) Response area to get (resulting equation): Using the Subtraction Property of Equality: Subtract \(15\) from both sides: \[ 2x + 15 - 15 = -3 - 15 \] Which simplifies to: \[ 2x = -18 \]

   Choose a property:
   Subtraction Property of Equality

   Response area:
   \( 2x = -18 \)

4. Use the (choose a property) Response area to get (resulting answer): Using the Division Property of Equality: Divide both sides by \(2\): \[ \frac{2x}{2} = \frac{-18}{2} \] Which simplifies to: \[ x = -9 \]

   Choose a property:
   Division Property of Equality

   Response area:
   \( x = -9 \)

So the final solutions inserted into the appropriate areas are:

1. \( 2x - 6 + 21 = -3 \)
2. \( 2x + 15 = -3 \)
3. Subtraction Property of Equality -> \( 2x = -18 \)
4. Division Property of Equality -> \( x = -9 \)