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54 800.852.2435 Moving with Algebra ©Math TeachersPress, Inc. 346 Solve the equation – 2 x – 1 = 3( x – 2) Solve each equation. Check your solutions. 1. – 2 x + 5 = 4 x – 7 4. 3( x – 1) = 4 + 5 x 7. – 4( x – 1) = 3( x – 1) 10. – x = 3(2 x – 7) 2. 3 x – 4 = 2 x – 3 5. – 5 x + 3 = x – 9 8. – x + 7 = – 4( x – 2) 11. 3(5 – x ) = 2 x – 5 3. x – 6 = – 7 x + 2 6. 3( x + 2) = – 5( x – 1) 9. – 2(3 x + 2) = – 4( x – 3) 12. – 3( x + 4) = 5( x + 2) Solve Equations with Variables on Both Sides – 2 x – 1 3( x – 2) = = + 2 x + 2 x = – 2 x – 1 3 x – 6 = = + 6 + 6 = – 1 5 x – 6 = = 5 5 x = = 1 x = = Use the distributive property to remove parentheses. Add + 2 x to both sides to get all variables on one side of the equation. Add + 6 to both sides. Divide both sides by5. 2 3 1 1 4 2 1 – 8 7—2 1—8 11—4 1—3 – – – Lesson Plans 346 Objective: To solve equations with variables on both sides of the equation. Materials: Plastic algebra tiles or paper algebra tiles made from Master 1 Equations with Variables on Both Sides Today we will learn how to solve equations that have variables on both sides of the equation. Write on the board: 2(2 – x ) = 3 x – 6 What is the first step in solving this equation? (Use the distributive property to get rid of the parentheses.) What is the equation that results? (4 – 2 x = 3 x – 6) Model each step of solving using algebra tiles and record using algebraic symbols. = 4 – 2 x = 3 x – 6 Remember we want to determine the value of x or +1 x . For this reason, we should add 2 x to both sides next. This will result in a positive value for x . Model this as shown below. = Hold up 1 positive rectangle and 1 negative rectangle. What is the value of – 1 x + 1 x , or x + – x ? (0) Yes, this is also a zero pair. Let’s remove the zero pairs from the equation. What equation results? (4 = 5 x – 6) = What is the next step in solving this equation? (Add +6 to both sides) Continue to model the solution steps using algebra tiles and recording them algebraically as well. The solution is x = 2. Write on the board: x – 4 = – 3(2 x – 1) What is the first step in solving this equation? (Use the distributive property to remove the parentheses.) Write the result on the board: x – 4 = – 6 x + 3. Ask students to model the equation with algebra tiles, and use the algebra tiles to solve the equation. Record the steps on the board. The solution is = 1. Read the example together at the top of the page. Remind students to remove the parentheses first. Skill Builders pp. 268, 269 Sample Lesson: Linear Functions, Equations and Inequalities (Equations with Variables) Solving equaƟons with variables on both sides of the equaƟon.