Questions: Solve the following equations. Complete parts (a) through (d) below. (a) 3x+9=9 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. x=0,-6 (Use a comma to separate answers as needed.) B. There is no real solution. (b) x-2=2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. x=4,0 (Use a comma to separate answers as needed.) B. There is no real solution. (c) 2x-4=4 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. x= (Use a comma to separate answers as needed.) B. There is no real solution.

Solve the following equations. Complete parts (a) through (d) below. (a) 3x+9=9 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. x=0,-6 (Use a comma to separate answers as needed.) B. There is no real solution. (b) x-2=2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. x=4,0 (Use a comma to separate answers as needed.) B. There is no real solution. (c) 2x-4=4 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. x= (Use a comma to separate answers as needed.) B. There is no real solution.
Transcript text: Solve the following equations. Complete parts (a) through (d) below. (a) $|3 x+9|=9$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $x=0,-6$ (Use a comma to separate answers as needed.) B. There is no real solution. (b) $|x-2|=2$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $x=4,0$ (Use a comma to separate answers as needed.) B. There is no real solution. (c) $|2 x-4|=4$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $x=$ $\square$ (Use a comma to separate answers as needed.) B. There is no real solution.
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Solution

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Solution Steps

Step 1: Solve \( |3x + 9| = 9 \)

The equation \( |3x + 9| = 9 \) can be split into two cases:

  1. \( 3x + 9 = 9 \)
    • Subtract 9 from both sides: \( 3x = 0 \)
    • Divide by 3: \( x = 0 \)
  2. \( 3x + 9 = -9 \)
    • Subtract 9 from both sides: \( 3x = -18 \)
    • Divide by 3: \( x = -6 \)

The solutions are \( x = 0, -6 \).
Correct choice: A. \( x = 0, -6 \)

Step 2: Solve \( |x - 2| = 2 \)

The equation \( |x - 2| = 2 \) can be split into two cases:

  1. \( x - 2 = 2 \)
    • Add 2 to both sides: \( x = 4 \)
  2. \( x - 2 = -2 \)
    • Add 2 to both sides: \( x = 0 \)

The solutions are \( x = 4, 0 \).
Correct choice: A. \( x = 4, 0 \)

Step 3: Solve \( |2x - 4| = 4 \)

The equation \( |2x - 4| = 4 \) can be split into two cases:

  1. \( 2x - 4 = 4 \)
    • Add 4 to both sides: \( 2x = 8 \)
    • Divide by 2: \( x = 4 \)
  2. \( 2x - 4 = -4 \)
    • Add 4 to both sides: \( 2x = 0 \)
    • Divide by 2: \( x = 0 \)

The solutions are \( x = 4, 0 \).
Correct choice: A. \( x = 4, 0 \)

Final Answer

(a) \(\boxed{x = 0, -6}\)
(b) \(\boxed{x = 4, 0}\)
(c) \(\boxed{x = 4, 0}\)

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