Quiz: Practice Questions on Solving Algebraic Expressions and Equations (set 2)

This quiz contains questions designed to test your understanding of the fundamentals of algebraic expressions and equations. The questions cover topics such as solving linear equations, solving quadratic equations, and simplifying algebraic expressions. Please refrain from using external resources to assist in solving the questions. If your answers are incorrect, you may retake the quiz and aim for a perfect score. If you notice any errors in the questions or answers, please leave a comment. Enjoy the quiz!

1. 
Simplify and find the value when x = 2 and y = -3: $2x^2 - 3xy + y^2 - (x^2 + 2xy - y^2$)

2. 
Factorize completely: $2x^3 + 5x^2 - 3x$

3. 
Solve: $3x^2 - 5x - 2 = 0$

4. 
Solve for x and y: $3x + 4y = 14$ and $5x - 2y = 8$

5. 
The length of a rectangle is 4 meters more than its width. The area of the rectangle is 96 $m^2$. Find its dimensions.

6. 
Solve: $\frac{2x + 3}{x - 1} = \frac{3x - 2}{x + 2}$

7. 
Simplify: $\frac{x^2 + 5x + 6}{x^2 - 9} \div \frac{x^2 + 2x}{x^2 - 4}$

8. 
Solve: $3^{(2x - 1)} = 81$

9. 
Solve for x: $\frac{x + 2}{x - 3} = \frac{x + 4}{x - 5}$

10. 
Solve for x: $\frac{1}{x + 2} + \frac{1}{x - 2} = \frac{2}{x² - 4}$

11. 
Solve for x: $3(x - 1) + 2(x + 4) = 5x + 7$

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