2. Single-Step Equations 33 22 11 Addition/Subtraction Multiplication/Division Substitution Simplifying Expressions

3. Solving Equations  When you solve an equation, you are isolating the variable to one side of the equal sign 2 www.themegallery.com

4. Order to Typically Follow  Addition and/or Subtraction  Multiplication and/or Division  This will typically minimize working with fractions unnecessarily 3 www.themegallery.com

5. Addition/Subtraction www.themegallery.com 4

6. to one side of an equation, When you do something

7. you have to do exactly the same thing to the other side.

8. To solve an equation means to find every number that makes the equation true.

9. In the equation, x is the number to get 15. you add to 7

10. What is the number? 8, of course.

11. What is the number? 8, of course.

12. What is the number? 8, of course. So we would write the solution,.

13. In some equations, the solution is obvious.

14. But in other equations, the solution is not so obvious.

15. Many times we need a way to solve equations.

16. 1.1. 2.2. 3.3. 4.4.

17. Multiplication/Division www.themegallery.com 16

18. Remember, To Solve an Equation means...  To isolate the variable having a coefficient of 1 on one side of the equation.  Ex: x = 5 is solved for x.  y = 2x - 1 is solved for y.

19. Multiplication Property of Equality  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.

20. An easy example: 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?

21. Let’s try another example! x = 4 2 Multiply each side by 2. (2)x = 4(2) 2 x = 8  Always check your solution!!  The original problem is x = 4 2  Using the solution x = 8, Is x/2 = 4?  YES! 4 = 4 and our solution is correct.

22.  The two negatives will cancel each other out.  The two fives will cancel each other out. (-5)  x = -15  Does -(-15)/5 = 3? What do we do with negative fractions? Recall that Solve. Multiply both sides by -5.

23. 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?

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

25. A fraction times a variable: 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 The one step method: Ex: 2x = 4 3 1. Multiply by the RECIPROCAL. (3)2x = 4(3) (2) 3 (2) x = 6

26. Try these on your own...

27. Evaluating Algebraic Expressions  Write the original expression  Substitute for each variable  Follow the Order of Operations 26

28. Evaluating Algebraic Expressions  Evaluate for a=-4, b=5 27

29. Evaluating Algebraic Expressions  Evaluate for x=1, y=1/2 28

30. Simplifying Algebraic Expressions  Like terms  Have the exact same variables (including powers)  Coefficients can be combined  Variables remain unchanged 29 Like Terms

31. Simplifying Algebraic Expressions  Identify like terms  Combine like terms  Rewrite expression 30

32. Simplifying Algebraic Equations Simplify 31