1. Equations & Inequalities

What is a conditional equation? Give an example.

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |2x - 1| + 3 = 3

Find all values of x such that y = 0. y = 1/(5x + 5) - 3/(x + 1) + 7/5

Decide whether each statement is true or false. The equation 5x=4x is an example of a contradiction.

In Exercises 67–70, find all values of x such that y = 0. $y = \(\frac{x + 6}{3x - 12}\) - \(\frac{5}{x - 4}\) - \(\frac{2}{3}\)$

Solve each equation. ∜(x-15)=2

Solve each problem. See Example 4. In planning her retirement, Kaya deposits some money at 2.5% interest, and twice as much money at 3%. Find the amount deposited at each rate if the total annual interest income is \$850.

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)

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. (x - 2)/2x + 1 = (x + 1)/x

After a 30% price reduction, you purchase a 50″ 4K UHD TV for \$245. What was the television's price before the reduction?

In Exercises 99–106, solve each equation. [(3 + 6)² ÷ 3] × 4 = - 54 x

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 3/(x + 4) - 7 = - 4/(x + 4)

Solve each problem. If a person invests \$500 at 2% simple interest for 4 yr, how much interest is earned?

After a 20% reduction, a 42-inch HDTV sold for \$256. What was the price before the reduction?