| Problem 1.When multiplying or dividing both sidesof an inequality by a positive number,the direction of the inequalitystays the same. | Problem 2.When multiplying or dividing both sidesof an inequality by a negative number,the direction of the inequalitymust be switched: < switches to >, etc. | |||
| Solve for x: | 10x + 4 < 7x + 19. | 2x + 4 < 7x -11 | ||
| Subtract 7x from both sides: | 10x + 4 - 7x < 7x + 19 - 7x. | 2x + 4 - 7x < 7x -11 - 7x | ||
| Simplify: | 3x + 4 < 19. | -5x + 4 < -11 | ||
| Subtract 4 from both sides: | 3x + 4 - 4 < 19 - 4. | -5x + 4 -4 < -11 - 4 | ||
| Simplify: | 3x < 15. | -5x < -15 | ||
| Divide: | 3x/3 < 15/3. | -5x/(-5) > -15/(-5) | ||
| Simplify: | x < 5. | x > 3 |
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