Lesson summary algebraic approach: to solve an equation algebraically means to use the properties of operations and if-then moves to simplify the equation into a form where the solution is easily recognizable. for the equations we are studying this year (called linear equations), that form is an equation that looks like = a number, where the number is the solution. if-then moves: if is a solution to an equation, it will continue to be a solution to the new equation formed by adding or subtracting a number from both sides of the equation. it will also continue to be a solution when both sides of the equation are multiplied by or divided by a nonzero number. we use these if-then moves to make zeros and ones in ways that simplify the original equation. useful first step: if one is faced with the task of finding a solution to an equation, a useful first step is to collect like terms on each side of the equation. problem set write and solve an equation for each problem. 1. the perimeter of a rectangle is 30 inches. if its length is three times its width, find the dimensions. 2. a cell phone company has a basic monthly plan of $40 plus $0.45 for any minutes used over 700. before receiving his statement, john saw he was charged a total of $48.10. write and solve an equation to determine how many minutes he must have used during the month. write an equation without decimals. 3. a volleyball coach plans her daily practices to include 10 minutes of stretching, 2 3 of the entire practice scrimmaging, and the remaining practice time working on drills of specific skills. on wednesday, the coach planned 100 minutes of stretching and scrimmaging. how long, in hours, is the entire practice? 4. the sum of two consecutive even numbers is 54. find the numbers. 5. justin has $7.50 more than eva, and emma has $12 less than justin. together, they have a total of $63.00. how much money does each person have? 6. barry’s mountain bike weighs 6 pounds more than andy’s. if their bikes weigh 42 pounds altogether, how much does barry’s bike weigh? identify the if-then moves in your solution. 7. trevor and marissa together have 26 t-shirts to sell. if marissa has 6 fewer t-shirts than trevor, find how many t-shirts trevor has. identify the if-then moves in your solution.