1. Equations & Inequalities

Match the equation in Column I with its solution(s) in Column II. x² = 25

Evaluate the discriminant for each equation. Then use it to determine the number of distinct solutions, and tell whether they are rational, irrational, or nonreal complex numbers. (Do not solve the equation.) See Example 9.

$9x^2+11x+4=0$

Solve each cubic equation using factoring and the quadratic formula. See Example 7.

$x^3+64=0$

Solve each equation. (x+4)(x+2) = 2x

Solve each equation using completing the square. 3x² - 9x + 7 = 0

For each equation, solve for x in terms of y. 2x² + 4xy - 3y² = 2

Solve each equation. 2x²+x-15 = 0

Evaluate the discriminant for each equation. Then use it to determine the number of distinct solutions, and tell whether they are rational, irrational, or nonreal complex numbers. (Do not solve the equation.) See Example 9.

$8x^2-72=0$

Solve each equation for the specified variable. (Assume no denominators are 0.) See Example 8.

$h=-16t^2+v_{0}t+s_0$, for t

Solve each equation using the square root property. (-2x + 5)² = -8

Use the following facts. If x represents an integer, then x+1 represents the next consecutive integer. If x represents an even integer, then x+2 represents the next consecutive even integer. If x represents an odd integer, then x+2 represents the next consecutive odd integer. Find two consecutive even integers whose product is 224.

Solve each equation using the square root property. 27 - x² = 0

Find all values of x satisfying the given conditions. y₁ = 2x/(x + 2), y₂ = 3/(x + 4), and y₁ + y₂ = 1

Use Choices A–D to answer each question. A. 3x² - 17x - 6 = 0 B. (2x + 5)² = 7 C. x² + x = 12 D. (3x - 1)(x - 7) = 0 Which equation is set up for direct use of the zero-factor property? Solve it.

Solve each equation using completing the square. x² - 7x + 12 = 0