1. { Solving Equations Slideshow 9, Mathematics Room 307, Mr Richard Sasaki

2.  Consider equations as a balance  Understand how to alter both sides of an equation  Being able to maintain balance and solve equations for an unknown Objectives

3. Equations, numerical or algebraic have to balance. Let’s have a look at an easy numeric example. Balancing Numeric Equations 44= Of course we have a balance here as 4 = 4. If we change the number… + 1 ≠ If the amount on the left changes, the amount on the right must also change.

4. Example Balancing Algebraic Equations 9= If these two expressions are equally balanced, what must x be? Yes, 6 of course…because 6 + 3 = 9. But for more complicated equations, this thought process isn’t enough. We have to alter, yet maintain a balance.

5. Example Altering Algebraic Equations Solve x + 3 = 9. We need to alter each equation so the unknown equals a number. In this case, x = ?. So to get from x + 3 to x, we need to subtract 3. x + 3x + 3x + 3x + 3 = 9 -3-3 x = 6

6. Example Solve 7x= 63. Altering Algebraic Equations 7x7x7x7x = 63 ÷7 ÷7 x = 9 We always do the opposite to whatever terms or coefficients are together with the unknown. If something is multiplied by it, we divide, if something is added to it, we subtract…and so-on.

7. Examples Solve x – 3 = 9. Solving Algebraic Equations x = 12 (We added three to each side) x = 20 (We multiplied each side by 4.) y = 6 (We subtracted 1 and then divided by 2.) * - It’s easiest to remove other terms first and then divide out the coefficient. x = ±4 (Plus or minus 4 as roots have two possible results. Try the worksheets!

8. Answers 6 1 7 5 6 8 50 12c = 600 600 ÷ 12 = 50 Yen 4 32 40 6 -4 1 ½ 5 -5 0 3 1100 Yen -2 -17 The notepad. (257 Yen) a 7 15 70 2 77 8 3 150 Yen or 175 Yen (depending on whether discount was before or after)

9. Other Algebraic Equations Example -3 -3

10. Let’s check to see if we can see a pattern. Other Algebraic Equations Solve each of the following. Hopefully you can see a pattern! Try to use this idea for the next worksheet!

11. Answers