1. Equations & Inequalities

Solve each equation in Exercises 1 - 14 by factoring.3x^2 + 12x = 0

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

Answer each question. Answer each question. Unknown NumbersUse 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 integers whose product is 110.

Answer each question. Answer each question. Answer each question. Unknown NumbersUse 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 168.

Use Choices A–D to answer each question. A. 3x^2 - 17x - 6 = 0 B. (2x + 5)^2 = 7 C. x^2 + x = 12 D. (3x - 1)(x - 7) = 0 Only one of the equations does not require Step 1 of the method for completing the square described in this section. Which one is it? Solve it.

Use Choices A–D to answer each question. A. 3x^2 - 17x - 6 = 0 B. (2x + 5)^2 = 7 C. x^2 + x = 12 D. (3x - 1)(x - 7) = 0Only one of the equations is set up so that the values of a, b, and c can be determined immediately. Which one is it? Solve it.

Answer each question. Answer each question. Answer each question. Unknown NumbersUse 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. The sum of the squares of two consecutive odd integers is 202. Find the integers

Solve each equation in Exercises 15–34 by the square root property.3x^2 = 27

Answer each question. Answer each question. Answer each question. Unknown NumbersUse 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. The sum of the squares of two consecutive even integers is 52. Find the integers.

Solve each equation in Exercises 15–34 by the square root property.5x^2 = 45

Solve each equation using the zero-factor property. See Example 1. 2x^2 - x = 15

Solve each equation using the zero-factor property. See Example 1. -6x^2 + 7x = -10

Solve each equation in Exercises 15–34 by the square root property.3x^2 - 1 = 47

Solve each equation in Exercises 15–34 by the square root property.2x^2 - 5 = - 55

Solve each problem. See Examples 1 and 2. Dimensions of a Square. The length of each side of a square is 3 in. more than the length of each side of a smaller square. The sum of the areas of the squares is 149 in.2. Find the lengths of the sides of the two squares.