Instructions
Complete the following algebra problems. Show all your work where necessary.
1. Solve for x in the equation:
3x + 5 = 20
2. Solve for y in the equation:
2y - 4 = 10
3. Simplify the algebraic expression:
4a + 3a - 2a + 5
4. Expand the expression:
(x + 3)(x - 2)
5. Factor the expression:
x² + 5x + 6
6. Word Problem:
A rectangle has a length that is 3 times its width. If the perimeter of the rectangle is 48 units, what are the dimensions of the rectangle? Write your answer using the format "width = x units, length = y units".
7. Bonus Challenge:
Consider the quadratic equation: x² - 4x - 5 = 0. Solve for x using the quadratic formula.
8. Reflection:
What strategies did you use to solve these problems? What did you find challenging?