Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
You solved one-step and multi-step inequalities. • Solve compound inequalities. • Solve absolute value inequalities. • compound inequality • intersection • union Solve an “And” Compound Inequality Solve 10 3y – 2 < 19. Graph the solution set on a number line. Method 1 Solve separately. Write the compound inequality using the word and. Then solve each inequality. 10 3y – 2 and 3y – 2 < 19 12 3y 3y < 21 4 y y<7 4y<7 Solve an “And” Compound Inequality Method 2 Solve both together. Solve both parts at the same time by adding 2 to each part. Then divide each part by 3. 10 3y – 2 < 19 12 3y < 21 4 y <7 Solve an “And” Compound Inequality Graph the solution set for each inequality and find their intersection. y4 y<7 4y<7 Answer: Solve an “And” Compound Inequality Graph the solution set for each inequality and find their intersection. y4 y<7 4y<7 Answer: The solution set is y | 4 y < 7. What is the solution to 11 2x + 5 < 17? A. B. C. D. What is the solution to 11 2x + 5 < 17? A. B. C. D. Solve an “Or” Compound Inequality Solve x + 3 < 2 or –x –4. Graph the solution set on a number line. Solve each inequality separately. x+3 <2 x < –1 or –x –4 x4 x < –1 x4 x < –1 or x 4 Answer: Solve an “Or” Compound Inequality Solve x + 3 < 2 or –x –4. Graph the solution set on a number line. Solve each inequality separately. x+3 <2 x < –1 or –x –4 x4 x < –1 x4 x < –1 or x 4 Answer: The solution set is x | x < –1 or x 4. What is the solution to x + 5 < 1 or –2x –6? Graph the solution set on a number line. A. B. C. D. What is the solution to x + 5 < 1 or –2x –6? Graph the solution set on a number line. A. B. C. D. Solve Absolute Value Inequalities A. Solve 2 > |d|. Graph the solution set on a number line. 2 > |d| means that the distance between d and 0 on a number line is less than 2 units. To make 2 > |d| true, you must substitute numbers for d that are fewer than 2 units from 0. Notice that the graph of 2 > |d| is the same as the graph of d > –2 and d < 2. All of the numbers between –2 and 2 are less than 2 units from 0. Answer: Solve Absolute Value Inequalities A. Solve 2 > |d|. Graph the solution set on a number line. 2 > |d| means that the distance between d and 0 on a number line is less than 2 units. To make 2 > |d| true, you must substitute numbers for d that are fewer than 2 units from 0. Notice that the graph of 2 > |d| is the same as the graph of d > –2 and d < 2. All of the numbers between –2 and 2 are less than 2 units from 0. Answer: The solution set is d | –2 < d < 2. A. What is the solution to |x| > 5? A. B. C. D. A. What is the solution to |x| > 5? A. B. C. D. B. What is the solution to |x| < 5? A. {x | x > 5 or x < –5} B. {x | –5 < x < 5} C. {x | x < 5} D. {x | x > –5} B. What is the solution to |x| < 5? A. {x | x > 5 or x < –5} B. {x | –5 < x < 5} C. {x | x < 5} D. {x | x > –5} Solve a Multi-Step Absolute Value Inequality Solve |2x – 2| 4. Graph the solution set on a number line. |2x – 2| 4 is equivalent to 2x – 2 4 or 2x – 2 –4. Solve each inequality. 2x – 2 4 or 2x – 2 –4 2x 6 2x –2 x3 x –1 Answer: Solve a Multi-Step Absolute Value Inequality Solve |2x – 2| 4. Graph the solution set on a number line. |2x – 2| 4 is equivalent to 2x – 2 4 or 2x – 2 –4. Solve each inequality. 2x – 2 4 or 2x – 2 –4 2x 6 2x –2 x3 x –1 Answer: The solution set is x | x –1 or x 3. What is the solution to |3x – 3| > 9? Graph the solution set on a number line. A. B. C. D. What is the solution to |3x – 3| > 9? Graph the solution set on a number line. A. B. C. D. Write and Solve an Absolute Value Inequality A. JOB HUNTING To prepare for a job interview, Hinda researches the position’s requirements and pay. She discovers that the average starting salary for the position is $38,500, but her actual starting salary could differ from the average by as much as $2450. Write an absolute value inequality to describe this situation. Let x = the actual starting salary. The starting salary can differ by as much as $2450. from the average |38,500 – x| Answer: 2450 Write and Solve an Absolute Value Inequality A. JOB HUNTING To prepare for a job interview, Hinda researches the position’s requirements and pay. She discovers that the average starting salary for the position is $38,500, but her actual starting salary could differ from the average by as much as $2450. Write an absolute value inequality to describe this situation. Let x = the actual starting salary. The starting salary can differ by as much as $2450. from the average |38,500 – x| Answer: |38,500 – x| 2450 2450 Write and Solve an Absolute Value Inequality B. JOB HUNTING To prepare for a job interview, Hinda researches the position’s requirements and pay. She discovers that the average starting salary for the position is $38,500, but her actual starting salary could differ from the average by as much as $2450. Solve the inequality to find the range of Hinda’s starting salary. | 38,500 – x | 2450 Rewrite the absolute value inequality as a compound inequality. Then solve for x. –2450 38,500 – x 2450 –2450 – 38,500 –x 2450 – 38,500 –40,950 –x –36,050 40,950 x 36,050 Write and Solve an Absolute Value Inequality Answer: Write and Solve an Absolute Value Inequality Answer: The solution set is x | 36,050 x 40,950. Hinda’s starting salary will fall within $36,050 and $40,950.