31) 3x^2 - 4x + 7 = x^2 - 5x + (-1 + 2x^2)

Solution:

• Simplify the right side of the equation: \( x^2 - 5x - 1 + 2x^2 = 3x^2 - 5x - 1 \)
• Set up the equation: \( 3x^2 - 4x + 7 = 3x^2 - 5x - 1 \)
• Subtract \( 3x^2 \) from both sides: \( -4x + 7 = -5x - 1 \)
• Add \( 5x \) to both sides: \( x + 7 = -1 \)
• Subtract 7 from both sides: \( x = -8 \)

Final Answer: x = -8