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12 + 3x = 36(1 point) Responses x=7 x=7 x=6 x=6 x=3 x=3 x=8 x=8 Question 2 x2 + 5 = 8 (1 point) Responses 4 4 6 6 30 30 1 1 Question 3 -2X + 3 = 25(1 point) Responses 22 22 11 11 -11 -11 10 10 Question 4 10x - 6 = 5x + 19(1 point) Responses -2 -2 5 5 -4 -4 1 1 Question 5 8x - 4 = 6x + 2(1 point) Responses x=3 x=3 x=8 x=8 x=2 x=2 x=10

1 answer

Let's solve each equation step by step:

Question 1:
\( 12 + 3x = 36 \)
Subtract 12 from both sides:
\( 3x = 24 \)
Divide by 3:
\( x = 8 \)

Question 2:
\( x^2 + 5 = 8 \)
Subtract 5 from both sides:
\( x^2 = 3 \)
Take the square root:
\( x = \sqrt{3} \) (approximately 1.732)
The closest integer option is not provided.

Question 3:
\( -2x + 3 = 25 \)
Subtract 3 from both sides:
\( -2x = 22 \)
Divide by -2:
\( x = -11 \)

Question 4:
\( 10x - 6 = 5x + 19 \)
Subtract \( 5x \) from both sides:
\( 5x - 6 = 19 \)
Add 6 to both sides:
\( 5x = 25 \)
Divide by 5:
\( x = 5 \)

Question 5:
\( 8x - 4 = 6x + 2 \)
Subtract \( 6x \) from both sides:
\( 2x - 4 = 2 \)
Add 4 to both sides:
\( 2x = 6 \)
Divide by 2:
\( x = 3 \)

Summary of Answers:

  1. \( x = 8 \)
  2. \( x = \sqrt{3} \) (approximately needs context on integer selection)
  3. \( x = -11 \)
  4. \( x = 5 \)
  5. \( x = 3 \)

Please check the integer responses for Question 2, as \( \sqrt{3} \) does not match any of the provided options.