2.  A.4f Apply these skills to solve practical problems.  A.4b Justify steps used in solving equations.  Use a graphing calculator to check your solutions. Objectives :

3.  To isolate the variable on one side of the equation.  Ex: x = 5 is solved for x.  y = 2x - 1 is solved for y.

4.  For any numbers a, b, and c, if a = b, then ac = bc. What it means: You can multiply BOTH sides of an equation by any number and the equation will still hold true.

5. We all know that 3 = 3. Does 3(4) = 3? NO! But 3(4) = 3(4). The equation is still true if we multiply both sides by 4.  Would you ever put deodorant under just one arm?  Would you ever put nail polish on just one hand?  Would you ever wear just one sock?

6.  Always check your solution!!  The original problem is x = 4 2  Using the solution x = 8, Does 8/2 = 4?  YES! 4 = 4 and our solution is correct. x = 4 2 Multiply each side by 2. (2)x = 4(2) 2 x = 8

7. Division Property of Equality For any numbers a, b, and c (c≠0), if a = b, then a/c = b/c What it means:  You can divide BOTH sides of an equation by any number, except zero, and the equation will still hold true.  Why did we add c ≠ 0?

8. 2) -6y = 18 Divide both sides by -6. -6y = 18 -6 -6 y = -3  Does -6(-3) = 18? YES! 1) 4x = 24 Divide both sides by 4. 4x = 24 4 4 x = 6  Does 4(6) = 24? YES!

9. The one step method: Ex: 2x = 4 3 1. Multiply by the reciprocal. 3 2x = 4 3 2 3 2 x = 6 The two step method: Ex: 2x = 4 3 1. Multiply by 3. (3)2x = 4(3) 3 2x = 12 2. Divide by 2. 2x = 12 2 2 x = 6

10. Solve -3v = -129 1. v = -126 2. v = -43 3. v = 43 4. v = 126 Answer Now

11. Which step clears the fraction in 1. Multiply by 3 2. Multiply by 5 3. Multiply by -12 4. Multiply by -5 Answer Now

12. Solve 1. b = -56 2. b = -14 3. b = 14 4. b = 56 Answer Now