# solving linear & quadratic equations

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1. 1. #SOLVED NA KO!
2. 2. Solving Linear & Quadratic Equations
3. 3. Review of Terms 1) Variable 2) Coefficient 3) Constant 4) Expression 5) Equation Throughout Algebra, you will hear many different terms being used to describe the parts of an equation or expression. You will need to know the definition of the following terms throughout the course.
4. 4. Review of Terms 1) Variable 2) Coefficient 3) Constant 4) Expression 5) Equation Variable: A letter which is used to represent an unknown number or value. Any letter can be used as a variable.
5. 5. Review of Terms 1) Variable 2) Coefficient 3) Constant 4) Expression 5) Equation Coefficient: The number in front of a variable in a mathematical equation or expression. The coefficient is actually being multiplied by the variable x3 Coefficient: 3 Means: 3 times x 2 4 1 x Coefficient: Means: times x2
6. 6. Review of Terms 1) Variable 2) Coefficient 3) Constant 4) Expression 5) Equation Constant: A number being added or subtracted from a variable in an equation or expression. 95 x The constant in the above expression is: -9
7. 7. Review of Terms 1) Variable 2) Coefficient 3) Constant 4) Expression 5) Equation Expression: Contains at least one variable. Examples: a 5+x zy 23
8. 8. Review of Terms 1) Variable 2) Coefficient 3) Constant 4) Expression 5) Equation Equation: A sentence that states that two mathematical expressions are equal. Examples: 2253 =x hrV 2 = 174132 += xx
9. 9. Steps to Solving Linear Equations 1. Simplify each side of the equation, if needed, by distributing or combining like terms. 2. Move variables to one side of the equation by using the opposite operation of addition or subtraction. 3. Isolate the variable by applying the opposite operation to each side. a. First, use the opposite operation of addition or subtraction. b. Second, use the opposite operation of multiplication or division. 4. Check your answer.
10. 10. Example X 5 = 4 X 5 + 5 = 4 + 5 X = 9
11. 11. Example X 7 = 13 X 7 + 7 = 13 + 7 X = 20
12. 12. Example 2X 3 = 7 2X 3 + 3 = 7 + 3 2X = 10 2 2 X = 5
13. 13. Example 5X + 4 = 9 5X + 4 - 4 = 9 - 4 5X = 5 5 5 X = 1
14. 14. Simplify: Use the distributive property STEPS TO SOLVINGSTEPS TO SOLVING: 1) Simplify 2) Move Variables 3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division 4) Check your answer 30)6(2)3(5 =++ xx EXAMPLE:
15. 15. Simplify: Combine like terms STEPS TO SOLVINGSTEPS TO SOLVING: 1) Simplify 2) Move Variables 3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division 4) Check your answer 30)6(2)3(5 =++ xx EXAMPLE: 30)122()155( =++ xx
16. 16. Isolate Variables: Undo the addition STEPS TO SOLVINGSTEPS TO SOLVING: 1) Simplify 2) Move Variables 3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division 4) Check your answer 30)6(2)3(5 =++ xx EXAMPLE: 30)122()155( =++ xx 3033 =+x
17. 17. Isolate Variables: Undo the multiplication STEPS TO SOLVINGSTEPS TO SOLVING: 1) Simplify 2) Move Variables 3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division 4) Check your answer 30)6(2)3(5 =++ xx EXAMPLE: 30)122()155( =++ xx 3033 =+x 273 =x
18. 18. Check your answer: Substitute the value of x back in STEPS TO SOLVINGSTEPS TO SOLVING: 1) Simplify 2) Move Variables 3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division 4) Check your answer 30)6(2)3(5 =++ xx EXAMPLE: 30)122()155( =++ xx 3033 =+x 9=x 273 =x
19. 19. STEPS TO SOLVINGSTEPS TO SOLVING: 1) Simplify 2) Move Variables 3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division 4) Check your answer 30)6(2)3(5 =++ xx EXAMPLE: 30)69(2)39(5 =++ 30)15(2)12(5 = 303060 = 3030 = The answer is true; therefore, the vale of x is true.
20. 20. Simplify: Use the distributive property STEPS TO SOLVINGSTEPS TO SOLVING: 1) Simplify 2) Move Variables 3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division 4) Check your answer )2(3)1(15 = xx EXAMPLE:
21. 21. Move Variables: Move the -15x to the other side of the equation. STEPS TO SOLVINGSTEPS TO SOLVING: 1) Simplify 2) Move Variables 3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division 4) Check your answer )2(3)1(15 = xx EXAMPLE: 631515 += xx
22. 22. Isolate Variables: Undo the addition STEPS TO SOLVINGSTEPS TO SOLVING: 1) Simplify 2) Move Variables 3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division 4) Check your answer )2(3)1(15 = xx EXAMPLE: 631515 += xx 61815 += x
23. 23. Isolate Variables: Undo the multiplication STEPS TO SOLVINGSTEPS TO SOLVING: 1) Simplify 2) Move Variables 3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division 4) Check your answer )2(3)1(15 = xx EXAMPLE: 631515 += xx 61815 += x x189 =
24. 24. Check your answer: Substitute the value of x back in STEPS TO SOLVINGSTEPS TO SOLVING: 1) Simplify 2) Move Variables 3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division 4) Check your answer )2(3)1(15 = xx EXAMPLE: 631515 += xx 61815 += x x189 = x= 2 1
25. 25. The answer is true; therefore, the vale of x is true. STEPS TO SOLVINGSTEPS TO SOLVING: 1) Simplify 2) Move Variables 3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division 4) Check your answer )2(3)1(15 = xx EXAMPLE: = 2 2 1 3 2 1 115 = 2 5 3 2 1 15 2 15 2 15 =
26. 26. Isolate Variables: Undo the addition STEPS TO SOLVINGSTEPS TO SOLVING: 1) Simplify 2) Move Variables 3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division 4) Check your answer 137 5 2 =+x EXAMPLE:
27. 27. Isolate Variables: Undo the division STEPS TO SOLVINGSTEPS TO SOLVING: 1) Simplify 2) Move Variables 3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division 4) Check your answer EXAMPLE: 137 5 2 =+x 6 5 2 =x
28. 28. Isolate Variables: Undo the multiplication STEPS TO SOLVINGSTEPS TO SOLVING: 1) Simplify 2) Move Variables 3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division 4) Check your answer EXAMPLE: 137 5 2 =+x 6 5 2 =x 302 =x
29. 29. Check your answer: Substitute the value of x back in STEPS TO SOLVINGSTEPS TO SOLVING: 1) Simplify 2) Move Variables 3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division 4) Check your answer EXAMPLE: 137 5 2 =+x 6 5 2 =x 302 =x 15=x
30. 30. The answer is true; therefore, the vale of x is true. STEPS TO SOLVINGSTEPS TO SOLVING: 1) Simplify 2) Move Variables 3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division 4) Check your answer EXAMPLE: 137 5 2 =+x 137 5 30 =+ 1376 =+ 1313 =
31. 31. Example
32. 32. Example 2 2
33. 33. STEPS TO SOLVINGSTEPS TO SOLVING QUADRATICQUADRATIC EQUATIONEQUATION: 1) Equate one side to 0. 2) Factor [solve for the zeros of the linear factors] Or use quadratic formula 3) Check your answer EXAMPLE: (x +6)(x -1) x = -6 x = 1
34. 34. Example
35. 35. Example
36. 36. Example
37. 37. Example
38. 38. Example
39. 39. For More Practice: Solve for x =
40. 40. Solve for x: 3X + 5 = 5X 3 30 seconds Time is up!!!
41. 41. Solve for x: 2x + 7 = 9x 4 30 seconds Time is up!!!
42. 42. Solve for x: x2 + 7x = 9x 1 30 seconds Time is up!!!
43. 43. Solve for x: 2x2 + 3x = x +12 60 seconds Time is up!!!