So, the solution set is a-∞, - 1 4 b ∪ a- 1 4 , ∞b . The graph is 1 4 – –5 –4 –3 –2 –1 0 1 2 3 4 5 Student Check 3 Solve each absolute value inequality. a. uxu <-4 b. uy - 8u ≤-1 c. uau >-3 d. u2b - 7u + 6 ≥ 3 e. ` 3x - 5 4 ` > 0 Applications Applications of absolute value inequalities arise when a certain quantity must have a certain distance from another quantity. Some examples are shown. Objective 4 Examples Solve each problem using an absolute value inequality. 4a. During the 2008 presidential election, one poll showed Obama leading McCain by 47% to 44%. This poll had a margin of error of 3%. According to the poll, what percent of votes would Obama actually get? (Source: www .foxnews.com) Solution 4a. Let p represent the percent of people who said they would vote for Obama. Since the margin of error is 3%, the absolute value of the difference between the percent surveyed and the actual percentage that voted for Obama is less than or equal to 3. So, we solve the following inequality. up - 47u ≤ 3 -3 ≤ p - 47 ≤ 3 -3 + 47 ≤ p - 47 + 47 ≤ 3 + 47 44≤ p ≤ 50 Based on the poll, Obama would have received between 44% and 50% of the votes. 4b. A hazardous chemical spill of titanium tetrachloride occurred at mile marker 331 on Interstate 40 in Tennessee. Emergency management personnel stated that motorists should be a minimum of 12 mi from the site of the spill. What are safe locations on Interstate 40 for motorists? Solution 4b. Let x represent the mile marker of a motorist. The distance from the site of the spill to the motorist should be at least 12 mi. Since motorists can be on either side of the spill, we must solve the following inequality. ux - 331u ≥ 12 x - 331 ≥ 12 or x - 331 ≤ -12 x - 331 + 331 ≥ 12 + 331 x - 331 + 331≤ -12 + 331 x ≥ 343 x ≤ 319 Motorists should be located at or below mile marker 319 or located at or above mile marker 343 to be a safe distance from the spill. Objective 4 ▶ Solve applications of absolute value inequalities. Apply property 1. Add 47 to each part. Simplify. Apply property 2. Add 331 to each side. Simplify. 130 Chapter 2 Linear Equations and Inequalities in One Variable
hendricks_intermediate_algebra_1e_ch1_3
To see the actual publication please follow the link above