1. Linear Equations in One Variable Objective: To find solutions of linear equations.

2. Linear Equations in One Variable An equation in x is a statement that two algebraic expressions are equal. For example, 3x – 5 = 7 is an equation.

3. Solutions of Equations To solve an equation in x means to find all values of x for which the equation is true. Such values are called solutions.

4. Solutions of Equations To solve an equation in x means to find all values of x for which the equation is true. Such values are called solutions. For instance, x = 4 is the solution of the equation 3x – 5 = 7 since replacing x with 4 makes a true statement.

5. Identity vs. Conditional Equation Identity- An equation that is true for every real number in the domain of the variable.

6. Identity vs. Conditional Equation Identity- An equation that is true for every real number in the domain of the variable. For example, is an identity since it is always true.

7. Identity vs. Conditional Equation Conditional Equation- An equation that is true for just some (or even none) of the real numbers in the domain of the variable.

8. Identity vs. Conditional Equation Conditional Equation- An equation that is true for just some (or even none) of the real numbers in the domain of the variable. For example, is conditional because x = 3 and x = -3 are the only solutions.

9. Definition of a Linear Equation A linear equation in one variable x is an equation that can be written in the standard form ax + b = 0, where a and b are real numbers and a cannot equal 0.

10. Example 1a Solve the following linear equation.

11. Example 1a Solve the following linear equation.

12. Example 1b You Try Solve the following linear equation.

13. Example 1b You Try Solve the following linear equation.

14. Example 2 Solve the following linear equations.

15. Example 2 Solve the following linear equations.

16. Example 2 Solve the following linear equations.

17. Linear Equations in other forms Some equations involve fractions. Our goal is to get rid of the fraction by multiplying by the common denominator.

18. Linear Equations in other forms Some equations involve fractions. Our goal is to get rid of the fraction by multiplying by the common denominator. The common denominator is 12. Multiply everything by 12.

19. Linear Equations in other forms Some equations involve fractions. Our goal is to get rid of the fraction by multiplying by the common denominator. The common denominator is 12. Multiply everything by 12.

20. Linear Equations in other forms You Try. Solve the following equation.

21. Linear Equations in other forms You Try. Solve the following equation.

22. Extraneous Solutions When multiplying or dividing an equation by a variable expression, it is possible to introduce an extraneous solution. An extraneous solution is one that you get by solving the equation but does not satisfy the original equation.

23. Example 4 Solve the following.

24. Example 4 Solve the following.

25. Example 4 Solve the following.

26. Example 4 Solve the following.

27. Example 4 Solve the following. If we try to replace each x value with x = -2, we will get a zero in the denominator of a fraction, which we cannot have. There are no solutions.

28. Example 4 You Try Solve the following.

29. Example 4 You Try Solve the following.

30. Intercepts To find the x-intercepts, set y equal to zero and solve for x.

31. Intercepts To find the x-intercepts, set y equal to zero and solve for x. To find the y-intercepts, set x equal to zero and solve for y.

32. Intercepts To find the x-intercepts, set y equal to zero and solve for x. To find the y-intercepts, set x equal to zero and solve for y. Find the x and y-intercepts for the following equation.

33. Intercepts To find the x-intercepts, set y equal to zero and solve for x. To find the y-intercepts, set x equal to zero and solve for y. Find the x and y-intercepts for the following equation. x-intercept (y = 0)

34. Intercepts To find the x-intercepts, set y equal to zero and solve for x. To find the y-intercepts, set x equal to zero and solve for y. Find the x and y-intercepts for the following equation. x-intercept (y = 0) y-intercept (x = 0)

35. Intercepts You Try Find the x and y-intercepts for the following equation.

36. Intercepts You Try Find the x and y-intercepts for the following equation. x-intercept (y = 0) y-intercept (x = 0)

37. Class work Pages 94-95 23, 25, 29, 31, 34, 35, 46, 47

38. Homework Pages 94-95 3-36, multiples of 3 45-53 odd 71,73,75