University:
Felician University
Course:
MATH-002 | Basic Math Skills-Algebra
Academic year:

2023
Views:

357

Pages:

3
Author:

GalacticGuru

Name: Key Date: Class: Solving Absolute-Value Equations and Inequalities Solve each equation. 1. |2x+1| = 7 2x+1 = 7 or 2x+1 = -7 2x = 6 or 2x = -8 x = 3 or x = -4 2. |7x| = 28 7x = 28 or 7x = -28 x = 4 or x = -4 3. 3|3x| = 9 |3x| = 3 3x = 3 or 3x = -3 x = 1 or x = -1 4. |5-2x| = 5 5-2x = 5 or 5-2x = -5 -2x = 0 or -2x = -10 x = 0 or x = 5 5. |11x-14| = 6 11x-14 = 6 or 11x-14 = -6 11x = 20 or 11x = 8 x = 20/11 or x = 8/11 6. |4-x| = 9 4-x = 9 or 4-x = -9 -x = 5 or -x = -13 x = -5 or x = 13 Solve each inequality or compound inequality. Then graph the solution. 7. |2x-10| ≤ 12 -12 ≤ 2x-10 ≤ 12 -2 ≤ 2x ≤ 22 -1 ≤ x ≤ 11 [Image of a number line with closed circles at -1 and 11, and a line segment connecting them] 8. 3|x-4| ≥ 12 |x-4| ≥ 4 x-4 ≥ 4 or -(x-4) ≥ 4 x ≥ 8 or x ≤ 0 [Image of a number line with closed circles at 0 and 8, and arrows pointing outward from both] 9. |9x| ≥ 18 9x ≥ 18 or -9x ≥ 18 x ≥ 2 or x ≤ -2 [Image of a number line with closed circles at -2 and 2, and arrows pointing outward from both] 10. |7x-3| ≥ 8 or 3x-7 ≤ 8 7x-3 ≥ 8 or 7x-3 ≤ -8 7x ≥ 11 or 7x ≤ -5 x ≥ 11/7 or x ≤ -5/7 [Image of a number line with closed circles at -5/7 and 11/7, and arrows pointing outward from both] 11. 0.3|x| ≤ 0.9 |x| ≤ 3 -3 ≤ x ≤ 3 [Image of a number line with closed circles at -3 and 3, and a line segment connecting them] 12. |7x-1| ≥ 21 AND |x+2| ≤ 3 7x-1 ≥ 21 or 7x-1 ≤ -21 7x ≥ 22 or 7x ≤ -20 x ≥ 22/7 or x ≤ -20/7 [Image of a number line with closed circles at -20/7 and 22/7, and arrows pointing outward from both] Solve. 13. Any measurement is accurate within ±0.5 of the measurement unit. For example, if you measure your pencil to the nearest inch, your measurement could be 0.5 inch too long or 0.5 inch too short. Write an absolute-value inequality that shows the maximum and minimum actual measure of a nail measured to be 4.4 centimeters to the nearest 0.1 centimeter. Name: Date: Class: Solving Absolute-Value Equations and Inequalities Solve each equation. 1. |2x-3| = 15 2x-3 = 15 or 2x-3 = -15 2x = 18 or 2x = -12 x = 9 or x = -6 2. |x+9| = 2 x+9 = 2 or x+9 = -2 x = -7 or x = -11 3. 11-|4-x| = 4 -11 + |4-x| = -4 |4-x| = 7 4-x = 7 or 4-x = -7 -x = 3 or -x = -11 x = -3 or x = 11 4. 5|7-2x| < 40 |7-2x| < 8 -8 < 7-2x < 8 -15 < -2x < -1 15/2 > x > 1/2 (1/2, 15/2) 5. 7x-6 ≤ 10 or 3(x+2) > 5x-8 7x ≤ 16 or 3x + 6 > 5x - 8 x ≤ 16/7 or -2x > -14 x ≤ 16/7 or x < 7 (-∞, 16/7) 6. |4x-1| ≥ 6 4x-1 ≥ 6 or 4x-1 ≤ -6 4x ≥ 7 or 4x ≤ -5 x ≥ 7/4 or x ≤ -5/4 (-∞, -5/4] U [7/4, ∞) 7. 3|5x-2| < 12 |5x-2| < 4 -4 < 5x-2 < 4 -2 < 5x < 6 -2/5 < x < 6/5 (-2/5, 6/5) 8. 2|3x-6| + 6 ≥ 24 2|3x-6| ≥ 18 |3x-6| ≥ 9 3x-6 ≥ 9 or 3x-6 ≤ -9 3x ≥ 15 or 3x ≤ -3 x ≥ 5 or x ≤ -1 (-∞, -1] U [5, ∞) 9. |9x+1|/4 < 2 |9x+1| < 8 -8 < 9x+1 < 8 -9 < 9x < 7 -1 < x < 7/9 (-1, 7/9) 10. Ben says that there is no solution for this absolute-value inequality. Is he correct? If not, solve the inequality. Explain how you know you are correct. 32 + |x-7| < 25 |x-7| < -7 He is correct. |x| is always positive or 0.