Solve each problem. See Example 1. The length of a rectangular label is 2.5 cm less than twice the width. The perimeter is 40.6 cm. Find the width.

Solve each equation using the zero-factor property. x² + 2x - 8 = 0

Solve each problem. See Example 1. The perimeter of a triangular plot of land is 2400 ft.The longest side is 200 ft less than twice the shortest. The middle side is 200 ft less than the longest side. Find the lengths of the three sides of the triangular plot.

Determine the values of the variable that cannot possibly be solutions of each equation. Do not solve. 1/(4x) - 2/x = 3

Solve each equation. | 5/ (x-3) | = 10

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. The sum of the squares of two consecutive odd integers is 202. Find the integers.

Solve each equation. $\frac{5}{6}x - 2x + \frac{4}{3} = \frac{5}{3}$

Solve each problem. (Modeling) Lead Intake As directed by the 'Safe Drinking Water Act' of December 1974, the EPA proposed a maximum lead level in public drinking water of 0.05 mg per liter. This standard assumed an individual consumption of two liters of water per day. If EPA guidelines are followed, write an equation that models the maximum amount of lead A ingested in x years. Assume that there are 365.25 days in a year.

Solve each problem. (Modeling) Online Retail Sales Projected retail e-commerce sales (in billions of dollars) for the years 2016–2022 can be modeled by the equation y=52.304x+396.80, where x=0 corresponds to 2016, x=1 corresponds to 2017, and so on. Based on this model, find projected retail e-commerce sales in 2022 to the nearest tenth of a billion. (Data from www.statista.com)

Solve each equation using the zero-factor property. 2x² - x = 15

Determine the values of the variable that cannot possibly be solutions of each equation. Do not solve. 5/(2x) - 2/x = 6

Solve each equation. |3/ (2x - 3) | = 4

Identify each number as real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions will apply.) -6 -2i

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. The sum of the squares of two consecutive even integers is 52. Find the integers.

Solve each equation. 3x+5 - 5(x+1)= 6x+7

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. The difference of the squares of two positive consecutive even integers is 84. Find the integers.

Solve each inequality. Give the solution set in interval notation. 3(x+5)+1≥5+3x

Solve each equation. See Example 1. (2x+5)/2 - 3x/(x-2) = x

Solve each equation. | (6x + 1)/ (x - 1) | = 3

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. The difference of the squares of two positive consecutive odd integers is 32. Find the integers.

Solve each equation. $\left| \frac{2x + 3}{3x - 4} \right| = 1$

Solve each equation using the zero-factor property. -6x² + 7x = -10

Solve each equation. (4x+3)/4 - 2x/(x+1) = x

Solve each inequality. Give the solution set in interval notation. 6x-(2x+3)≥4x-5

Identify each number as real, complex, pure imaginary, or nonreal com-plex. (More than one of these descriptions will apply.) √24

Solve each equation. x/(x-3) = 3/(x-3) + 3

Solve each inequality. Give the solution set in interval notation. 8x-3x+2<2(x+7)

Perform each operation. Write answers in standard form. (6-i) + (7-2i)

Solve each equation. x/(x-4) = 4/(x-4) + 4

Solve each equation. 4[2x-(3-x)+5] = -6x - 28