156 CHAPTER 1 Equations and Inequalities 1x + 121-4x2 + 1x - 124 = -8 Divide out common factors. -4x2 - 4x + 4x - 4 = -8 Distributive property -4x2 + 4 = 0 Write in standard form. x2 - 1 = 0 Divide by -4. 1x + 121x - 12 = 0 Factor. x + 1 = 0 or x - 1 = 0 Zero-factor property x = -1 or x = 1 Proposed solutions Neither proposed solution is valid, so the solution set is ∅. S Now Try Exercises 25 and 27. (b) -4x x - 1 + 4 x + 1 = -8 x2 - 1 -4x x - 1 + 4 x + 1 = -8 1x + 121x - 12 Factor. The restrictions on x are x ≠{1. Multiply by the LCD, 1x + 121x - 12. 1x + 121x - 12a -4x x - 1b + 1x + 121x - 12a 4 x + 1b = 1x + 121x - 12a -8 1x + 121x - 12 b PROBLEM-SOLVING HINT If a job can be completed in t units of time, then the rate of work, r, is 1 t of the job per unit time. r = 1 t The amount of work completed, A, is found by multiplying the rate of work, r, and the amount of time worked, t. This formula is similar to the distance formula d = rt. Amount of work completed =rate of work : amount of time worked or A =rt Work Rate Problems If a job can be completed in 3 hr, then the rate of work is 1 3 of the job per hr. After 1 hr the job would be 1 3 complete, and after 2 hr the job would be 2 3 complete. In 3 hr the job would be 3 3 complete, meaning that 1 complete job had been accomplished. EXAMPLE 3 Solving a Work Rate Problem One printer can do a job twice as fast as another. Working together, both printers can do the job in 2 hr. How long would it take each printer, working alone, to do the job? SOLUTION Step 1 Read the problem. We must find the time it would take each printer, working alone, to do the job. Step 2 Assign a variable. Let x represent the number of hours it would take the faster printer, working alone, to do the job. The time for the slower printer to do the job alone is then 2x hours.
RkJQdWJsaXNoZXIy NjM5ODQ=