Algebra I Guided Notes: Solving Equations and Inequalities with Variables on Both Sides Lesson 2.4/3.4 Objective: to solve equations and inequalities with variables on both sides If there is a variable on both sides of the equation/inequality, (ISOLATE THE VARIABLE!) 1. 2. 3. 4. 5. Distribute, combine like terms on each individual side. Add or subtract to move the variable to the one side. Add or subtract to move the constants to the other side. Solve the equation/inequality. **Remember with inequalities to switch the inequality sign if multiplying or dividing both sides by a negative. Examples 1) 6x + 3 = 4x + 9 2) - 5 + 3x = 5 + 2 x 3) x + 13 = 6 x - 2 4) 4(x + 1) = 2 x - 2 5) - 2(3z - 4) = 10 - 6 z 6) - 2(3z - 4) = 8 - 6 z Special Case: No Solution: true. 3x – 2 = 6 + 3x no value of the variable can make the equation Special Case: Identity: 3x + 6 = 6 + 3x true for every possible value of the variable 7) 3x + 7 > x – 5 8) 9) 8x – 7 + 2x < 4x + 11 10) 3(x – 5) > 6x + 9 3(x – 4) > 3x + 7