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Linear Equations in One Variable

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

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Linear Equations in One Variable

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  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 variablex 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

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