See attached file for full problem description.
1. Graph the inequality. 2x + 3y > 6
2. Given g(x) = -3x + 5, find g(2a)
3. Graph the inequality: x - y < = 2
4. Graph the inequality: y > =3x
5. Given f(x) = -x^3 - 3x^2 -3x +9, find f(-2), f(0), and f(3)
6. Given f(x) = -5x - 1, find f(-2)
7. Graph f(x) = 4x + 1
8. Graph f(x) = -2x+ 4
9. Solve the system by addition: 5x - 3y = 13, 4x - 3y = 11
10. Solve the system by substitution: x + y = 12, y = 2x
11. Adult tickets for a play cost $20 and child tickets cost $12. If there were 23 people at a performance and the theater collected $348 from ticket sales, how many adults and how many children attended the play?
12. A home-based company produces both hand-knitted scarves and sweaters. The scarves take 2 hours of labor to produce, and the sweaters take 14 hours. The labor available is limited to 40 hours per week, and the total production capacity is 5 items per week. Write a system of inequalities representing this situation, where x is the number of scarves and y is the number of sweaters. Then graph the system of inequalities.
13. The sum of two numbers is 34. Their difference is 12. What are the two numbers?
Assume the two numbers are x and y.
14. Solve the system by substitution: 3x - 5y = 15, y = 2x + 11
15. Solve the system by substitution: 3x - y = -7, x + y = -9
16. The sum of two numbers is 49. The second is 5 more than 3 times the first. What are the two numbers?
17. The difference of two numbers is 75. The second is 5 less than 5 times the first. What are the two numbers?
18. Solve the following system of linear inequalities by graphing: x - 3y >6, 3x + 2y >12
19. Given f(x) = x^2 + x + 10, find f(0)
20. Rewrite the equation y = -2x + 5 as a function of x
The solution shows how to graph inequality in xy-plane and solve system of equations in detail.