|x - 3| > 4 or |x| < 3
Solve your assigned inequality. These problems are mostly from my Linear Inequalities handout. The solutions are already listed on the bottom of the handout, therefore make sure that you show the steps.
You may use <= for less than or equal to, and >= for greater than or equal to. Be sure and look at your answer on the discussion board before you submit it. You can do this by clicking Preview. If your solution does not display the way you intended it to, click Back and then change from Smart Text to Plain Text. Plain Text will probably solve the display problem.
| Roadrunner | (5x + 3)/2 > 9 or 3x - 4 < 11 |
| Minnie | 3x - 4 ≤ 17 or 5 -2x ≤ -13 |
| Mickey | |4 - x| < 2 or |x| ≥ 5 |
| Speedy Gonzales | (4x - 8)/2 < 6 or 40 - 7x < 5 |
| Petunia Pig | (1/2)(x - 5) + 2 ≥ 10 and 3x - 4 > 8 |
| She Devil | 3x - 4 ≤ 17 and 5 -2x ≤ -13 |
| Goofy | |3 - 2x| ≤ 5 and |x| ≥ 1 |
| Yosemite Sam | 2x - 4 > 7 and 3 - x/2 < 1 |
| Tweety Bird | (4x - 8)/2 < 6 and 40 - 7x < 5 |
| Pluto | 2x - 4 > 7 or 3 - x/2 < 1 |
| Porky Pig | (5x + 3)/2 > 9 or 3x - 4 < 11 |
| Donald | |2 - x| ≥ 3 and |2x - 1| ≤ 9 |
| Sylvester | |3x - 5| > 4 and |x| < 5 |
| Elmer Fudd | 5x + 6 ≤ 1 and 5(x + 2) - 2 ≥ 3 |
| Pepe Le Pew | |3 - 2x| > 5 or |x| < 1 |
| Wile E. Coyote | (5x + 3)/2 > 9 and 3x - 4 < 11 |
| Henery Hawk | (5x + 3)/2 < 9 or 3x - 4 > 11 |
| Marc Anthony | 3x - 4 ≥ 17 or 5 -2x ≥ -13 |
| Tazmanian Devil | 3x - 4 ≥ 17 and 5 -2x ≥ -13 |
| Foghorn Leghorn | |4 - x| < 2 and |x| ≥ 5 |
| Daffy Duck | |4 - x| > 2 or |x| ≤ 5 |
| Chip | (4x - 8)/2 ≥ 6 and 40 - 7x ≥ 5 |
| Dale | (1/2)(x - 5) + 2 ≤ 10 and 3x - 4 < 8 |
| Marvin the Martian | |3 - 2x| ≥ 5 and |x| ≤ 1 |
| Bugs Bunny | 2x - 4 < 7 and 3 - x/2 > 1 |
| First solve each part separately, putting each part in brackets to avoid confusion. Note: the left hand absolute value inequality has a greater than sign so it ends up being two separate inequalities with an or statement. The right hand absolute value inequality has a less than sign so it ends up being one compound statement. | [x - 3 > 4 or x - 3 < -4] and [-3 < x < 3] |
| Simplify the left hand and right hand inequality statements. | [x > 7 or x < -1] and [-3 < x < 3] |
| Draw a picture to help figure out the solution. In this case we want the overlap of the two inequalities since they are joined by an 'and' statement. You don't have to show the picture in your solution, but please show everything else. | |
| Since this inequality was joined by an 'and' statement, the solution is the overlap of the other two inequalities. | Solution: [-3, -1) |
| If the problem had and 'or' instead of 'and': |x - 3| > 4 or |x| < 3 |
The solution would have been (-¥, 3]È(7, ¥) |