This document discusses how manipulating inequalities through addition, subtraction, multiplication, and division affects the inequality sign. It notes that adding or subtracting a number to both sides of an inequality, or multiplying/dividing both sides by a positive number, does not change the inequality. However, multiplying or dividing both sides of an inequality by a negative number requires flipping the inequality sign. It provides examples to illustrate these principles and concludes by presenting two inequalities to solve.

1. Inequalities 2 < 5 TRUE What if I add/subtract a number to both sides? +3 +3 TRUE 5 < 8 -12 -12 -7 < -4 TRUE Does adding or subtracting change the Inequality?

2. Inequalities So if we have x + 4 < 10 we can solve by subtracting 4 from each side and the inequality doesn’t change. -4 -4 x < 6

3. Inequalities 2 < 5 TRUE What if I multiply/divide a positive number to both sides? *10 *10 TRUE 20 < 50 10 < 25 TRUE Does multiplying/dividing by a positive number change the inequality? 2 2

4. Inequalities 2 < 5 TRUE What if I multiply/divide a negative number to both sides? *-10 *-10 FALSE -20 < -50 What do we have to do with the inequality sign if we multiply by a negative number? -20 > -50

5. Inequalities What if I multiply/divide a positive number to both sides? TRUE 20 < 50 -10 < -25 FALSE Does dividing by a negative number change the inequality? -2 -2

6. Inequalities What if I multiply/divide a positive number to both sides? TRUE 20 < 50 -2 -2 -10 < -25 FALSE What do we have to do with the inequality sign if we divide by a negative number? -10 > -25

7. Solve the inequality -7x + 8 < 22

8. Solve the inequality & graph -4(3 +x) < 2x +10