2.2 Solving Inequalities Using Addition or Subtraction

Solving for the variable Simplify the inequality Distribute, if needed Combine like terms, if needed The properties of equality also stand for inequalities. So, use inverse operations to isolate the variable. The inequality sign will not change.

Example 1 Solve the inequality x + 3 > 4, then graph the solution. - 3 - 3 x > 1

Try this… a.) x + 3 > 5 -3 -3 x > 2 b.) x – 2 > 7 + 2 + 2 -3 -3 x > 2 b.) x – 2 > 7 + 2 + 2 x > 9

Example 2 Solve the inequality 3y + 1 – 2y < -3, then graph the solution. 3y + 1 – 2y < -3 y + 1 < -3 (combine like terms) - 1 -1 y < -4

Try this… c.) 5y + 2 -4y < -1 y < -3

Example 3 Solving Real-Life Problems A circuit overloads at 1800 watts of electricity. You plug a microwave oven that uses 1100 watts of electricity into the circuit. Write and solve an inequality that represents how many watts you can add to the circuit without overloading it. 1100 + w <1800 w = additional watts -1100 -1100 w <700

Example 3 Continued Appliance Watts Radio 50 Blender 300 Hot Plate Solving Real-Life Problems A circuit overloads at 1800 watts of electricity. You plug a microwave oven that uses 1100 watts of electricity into the circuit. b) In addition to the microwave oven, which of the following appliances can you plug into the circuit at the same time without overloading the circuit? Since you can plug up to 700 watts into the circuit without overloading it, you can also plug in the blender and the radio. Appliance Watts Radio 50 Blender 300 Hot Plate 1200 Toaster 800

You try! The microwave oven only uses 1000 watts of electricity. Does this allow you to have the microwave oven and toaster plugged in at the same time? Explain. No, the circuit overloads at 1800 watts. The amount of electricity plugged into the circuit must be less than 1800, not equal to.