1.5 Balancing Equations

Review Fill in the following tables m 6m - 3 5 10 15 20 x 4x 2 16 24 8

Problems Robin’s hiking club charges a flat rate of $10 to join. The club also charges $2 for each hike. How can you make a table of values to show the cost of hiking with Robin’s club?  A rock climbing club charges an annual fee of $100. They also charge $5 an hour for each hour of climbing. Make a table of values to show the cost for 15 to 20 hours of climbing.

Equations An equation is a math sentence that has an equal sign and both sides are the same EX: 3 – 1 = 2 2a = 16

Commutative Property Commutative Property: changing the order of the problem doesn’t change the answer EX: 2 + 3 = 3 + 2 Addition and multiplication are commutative, subtraction and division are not.

Example Which of these shows the commutative property? A) 3 x 6 = 3 x 6 B) 3 x 6 = 6 x 3 C) 3 x 1 = 1 D) 6 ÷ 3 = 3 ÷ 6

Solving Equations How to solve an equation: Work out what to remove to get the variable alone Remove it by doing the opposite Do the same thing to the other side Important: Always remember to preserve equality, whatever you do to one side, you must do to the other!

Example We want to remove the – 2 Do the opposite (Opposite of – 2 is + 2) Do the same thing to the other side

Keep it Balanced Why do we add 2 to each side? To keep the balance In Balance Out of balance In balance again