30) -3x^2 + 5x - 3 = -x^2 + 3x + (2 - 2x^2)

Solution:

• Simplify the right side of the equation: \( -x^2 + 3x + 2 - 2x^2 = -3x^2 + 3x + 2 \)
• Set up the equation: \( -3x^2 + 5x - 3 = -3x^2 + 3x + 2 \)
• Add \( 3x^2 \) to both sides: \( 5x - 3 = 3x + 2 \)
• Subtract \( 3x \) from both sides: \( 2x - 3 = 2 \)
• Add 3 to both sides: \( 2x = 5 \)
• Divide by 2: \( x = \frac{5}{2} \)

Final Answer: x = \(\frac{5}{2}\)