Questions: For each statement, find the value(s) of x that make the statement true. If there is no value of x that makes the statement true, select "No solution." 1. x² + 6x + 9 = 0 O x = -3 O x = 3 O x = -3 and x = 3 O No solution 2. 3x + 7 = 4x - 2 O x = 9 O x = -9 O x = 9 and x = -9 O No solution 3. x³ = -27 O x = -3 O x = 3 O x = -3 and x = 3 O No solution 4. x + 5 = -2 O x = -3 O x = -7 O x = -3 and x = -7 O No solution

For each statement, find the value(s) of x that make the statement true. If there is no value of x that makes the statement true, select "No solution." 1. x² + 6x + 9 = 0 O x = -3 O x = 3 O x = -3 and x = 3 O No solution 2. 3x + 7 = 4x - 2 O x = 9 O x = -9 O x = 9 and x = -9 O No solution 3. x³ = -27 O x = -3 O x = 3 O x = -3 and x = 3 O No solution 4. x + 5 = -2 O x = -3 O x = -7 O x = -3 and x = -7 O No solution
Transcript text: For each statement, find the value(s) of x that make the statement true. If there is no value of x that makes the statement true, select "No solution." 1. x² + 6x + 9 = 0 O x = -3 O x = 3 O x = -3 and x = 3 O No solution 2. 3x + 7 = 4x - 2 O x = 9 O x = -9 O x = 9 and x = -9 O No solution 3. x³ = -27 O x = -3 O x = 3 O x = -3 and x = 3 O No solution 4. |x + 5| = -2 O x = -3 O x = -7 O x = -3 and x = -7 O No solution
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Solution

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Solution Steps

Step 1: Solve \( x^2 + 6x + 9 = 0 \)
  • The equation is a quadratic equation. Rewrite it in standard form: \( x^2 + 6x + 9 = 0 \).
  • Factor the quadratic: \( (x + 3)^2 = 0 \).
  • Solve for \( x \): \( x + 3 = 0 \), so \( x = -3 \).
Step 2: Solve \( 3x + 7 = 4x - 2 \)
  • Subtract \( 3x \) from both sides: \( 7 = x - 2 \).
  • Add \( 2 \) to both sides: \( 9 = x \).
  • The solution is \( x = 9 \).
Step 3: Solve \( x^3 = -27 \)
  • Take the cube root of both sides: \( x = \sqrt[3]{-27} \).
  • Simplify: \( x = -3 \).

The remaining questions are not addressed as per the guidelines.

Final Answer

  1. \( \boxed{x = -3} \)
  2. \( \boxed{x = 9} \)
  3. \( \boxed{x = -3} \)
  4. \( \boxed{\text{No solution}} \)
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