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# 2 5literal equations

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### 2 5literal equations

1. 1. Literal Equations
2. 2. Given an equation with many variables, to solve for a particular variable means to isolate that variable to one side of the equation. Literal Equations
3. 3. Given an equation with many variables, to solve for a particular variable means to isolate that variable to one side of the equation. We do this, just as solving equations in x, Literal Equations
4. 4. Given an equation with many variables, to solve for a particular variable means to isolate that variable to one side of the equation. We do this, just as solving equations in x, by +, –, * , / the same quantities to both sides of the equations. Literal Equations
5. 5. Given an equation with many variables, to solve for a particular variable means to isolate that variable to one side of the equation. We do this, just as solving equations in x, by +, –, * , / the same quantities to both sides of the equations. These quantities may be numbers or variables. Literal Equations
6. 6. Given an equation with many variables, to solve for a particular variable means to isolate that variable to one side of the equation. We do this, just as solving equations in x, by +, –, * , / the same quantities to both sides of the equations. These quantities may be numbers or variables. Example A. a. Solve for x if x + b = c Literal Equations
7. 7. Given an equation with many variables, to solve for a particular variable means to isolate that variable to one side of the equation. We do this, just as solving equations in x, by +, –, * , / the same quantities to both sides of the equations. These quantities may be numbers or variables. Example A. a. Solve for x if x + b = c Remove b from the LHS by subtracting from both sides x + b = c Literal Equations
8. 8. Given an equation with many variables, to solve for a particular variable means to isolate that variable to one side of the equation. We do this, just as solving equations in x, by +, –, * , / the same quantities to both sides of the equations. These quantities may be numbers or variables. Example A. a. Solve for x if x + b = c Remove b from the LHS by subtracting from both sides x + b = c –b –b Literal Equations
9. 9. Given an equation with many variables, to solve for a particular variable means to isolate that variable to one side of the equation. We do this, just as solving equations in x, by +, –, * , / the same quantities to both sides of the equations. These quantities may be numbers or variables. Example A. a. Solve for x if x + b = c Remove b from the LHS by subtracting from both sides x + b = c –b –b x = c – b Literal Equations
10. 10. Given an equation with many variables, to solve for a particular variable means to isolate that variable to one side of the equation. We do this, just as solving equations in x, by +, –, * , / the same quantities to both sides of the equations. These quantities may be numbers or variables. Example A. a. Solve for x if x + b = c Remove b from the LHS by subtracting from both sides x + b = c –b –b x = c – b b. Solve for w if yw = 5. Literal Equations
11. 11. Given an equation with many variables, to solve for a particular variable means to isolate that variable to one side of the equation. We do this, just as solving equations in x, by +, –, * , / the same quantities to both sides of the equations. These quantities may be numbers or variables. Example A. a. Solve for x if x + b = c Remove b from the LHS by subtracting from both sides x + b = c –b –b x = c – b b. Solve for w if yw = 5. Remove y from the LHS by dividing both sides by y. yw = 5 Literal Equations
12. 12. Given an equation with many variables, to solve for a particular variable means to isolate that variable to one side of the equation. We do this, just as solving equations in x, by +, –, * , / the same quantities to both sides of the equations. These quantities may be numbers or variables. Example A. a. Solve for x if x + b = c Remove b from the LHS by subtracting from both sides x + b = c –b –b x = c – b b. Solve for w if yw = 5. Remove y from the LHS by dividing both sides by y. yw = 5 yw/y = 5/y Literal Equations
13. 13. Given an equation with many variables, to solve for a particular variable means to isolate that variable to one side of the equation. We do this, just as solving equations in x, by +, –, * , / the same quantities to both sides of the equations. These quantities may be numbers or variables. Example A. a. Solve for x if x + b = c Remove b from the LHS by subtracting from both sides x + b = c –b –b x = c – b b. Solve for w if yw = 5. Remove y from the LHS by dividing both sides by y. yw = 5 yw/y = 5/y w = 5 y Literal Equations
14. 14. Literal Equations Adding or subtracting a term to both sides may be viewed as moving the term across the " = " and change its sign.
15. 15. To solve for a specific variable in a simple literal equation, do the following steps. Literal Equations Adding or subtracting a term to both sides may be viewed as moving the term across the " = " and change its sign.
16. 16. To solve for a specific variable in a simple literal equation, do the following steps. 1. If there are fractions in the equations, multiple by the LCD to clear the fractions. Literal Equations Adding or subtracting a term to both sides may be viewed as moving the term across the " = " and change its sign.
17. 17. To solve for a specific variable in a simple literal equation, do the following steps. 1. If there are fractions in the equations, multiple by the LCD to clear the fractions. 2. Isolate the term containing the variable we wanted to solve for Literal Equations Adding or subtracting a term to both sides may be viewed as moving the term across the " = " and change its sign.
18. 18. To solve for a specific variable in a simple literal equation, do the following steps. 1. If there are fractions in the equations, multiple by the LCD to clear the fractions. 2. Isolate the term containing the variable we wanted to solve for – move all the other terms to other side of the equation. Literal Equations Adding or subtracting a term to both sides may be viewed as moving the term across the " = " and change its sign.
19. 19. To solve for a specific variable in a simple literal equation, do the following steps. 1. If there are fractions in the equations, multiple by the LCD to clear the fractions. 2. Isolate the term containing the variable we wanted to solve for – move all the other terms to other side of the equation. 3. Isolate the specific variable by dividing the rest of the factor to the other side. Literal Equations Adding or subtracting a term to both sides may be viewed as moving the term across the " = " and change its sign.
20. 20. To solve for a specific variable in a simple literal equation, do the following steps. 1. If there are fractions in the equations, multiple by the LCD to clear the fractions. 2. Isolate the term containing the variable we wanted to solve for – move all the other terms to other side of the equation. 3. Isolate the specific variable by dividing the rest of the factor to the other side. Literal Equations Example B. a. Solve for x if (a + b)x = c Adding or subtracting a term to both sides may be viewed as moving the term across the " = " and change its sign.
21. 21. To solve for a specific variable in a simple literal equation, do the following steps. 1. If there are fractions in the equations, multiple by the LCD to clear the fractions. 2. Isolate the term containing the variable we wanted to solve for – move all the other terms to other side of the equation. 3. Isolate the specific variable by dividing the rest of the factor to the other side. Literal Equations Example B. a. Solve for x if (a + b)x = c (a + b) x = c div the RHS by (a + b) Adding or subtracting a term to both sides may be viewed as moving the term across the " = " and change its sign.
22. 22. To solve for a specific variable in a simple literal equation, do the following steps. 1. If there are fractions in the equations, multiple by the LCD to clear the fractions. 2. Isolate the term containing the variable we wanted to solve for – move all the other terms to other side of the equation. 3. Isolate the specific variable by dividing the rest of the factor to the other side. Literal Equations Example B. a. Solve for x if (a + b)x = c (a + b) x = c x = c (a + b) div the RHS by (a + b) Adding or subtracting a term to both sides may be viewed as moving the term across the " = " and change its sign.
23. 23. b. Solve for w if 3y2w = t – 3 Literal Equations
24. 24. b. Solve for w if 3y2w = t – 3 3y2w = t – 3 div the RHS by 3y2 Literal Equations
25. 25. b. Solve for w if 3y2w = t – 3 3y2w = t – 3 w = t – 3 3y2 div the RHS by 3y2 Literal Equations
26. 26. b. Solve for w if 3y2w = t – 3 3y2w = t – 3 c. Solve for a if b2 – 4ac = 5 w = t – 3 3y2 div the RHS by 3y2 Literal Equations
27. 27. b. Solve for w if 3y2w = t – 3 3y2w = t – 3 c. Solve for a if b2 – 4ac = 5 b2 – 4ac = 5 w = t – 3 3y2 div the RHS by 3y2 move b2 to the RHS Literal Equations
28. 28. b. Solve for w if 3y2w = t – 3 3y2w = t – 3 c. Solve for a if b2 – 4ac = 5 b2 – 4ac = 5 – 4ca = 5 – b2 w = t – 3 3y2 div the RHS by 3y2 move b2 to the RHS Literal Equations
29. 29. b. Solve for w if 3y2w = t – 3 3y2w = t – 3 c. Solve for a if b2 – 4ac = 5 b2 – 4ac = 5 – 4ca = 5 – b2 w = t – 3 3y2 div the RHS by 3y2 move b2 to the RHS div the RHS by –4c Literal Equations
30. 30. b. Solve for w if 3y2w = t – 3 3y2w = t – 3 c. Solve for a if b2 – 4ac = 5 b2 – 4ac = 5 – 4ca = 5 – b2 w = t – 3 3y2 a = 5 – b2 –4c div the RHS by 3y2 move b2 to the RHS div the RHS by –4c Literal Equations
31. 31. b. Solve for w if 3y2w = t – 3 3y2w = t – 3 c. Solve for a if b2 – 4ac = 5 b2 – 4ac = 5 – 4ca = 5 – b2 w = t – 3 3y2 a = 5 – b2 –4c div the RHS by 3y2 move b2 to the RHS div the RHS by –4c Literal Equations d. Solve for y if a(x – y) = 10
32. 32. b. Solve for w if 3y2w = t – 3 3y2w = t – 3 c. Solve for a if b2 – 4ac = 5 b2 – 4ac = 5 – 4ca = 5 – b2 w = t – 3 3y2 a = 5 – b2 –4c div the RHS by 3y2 move b2 to the RHS div the RHS by –4c Literal Equations d. Solve for y if a(x – y) = 10 a(x – y) = 10 expand
33. 33. b. Solve for w if 3y2w = t – 3 3y2w = t – 3 c. Solve for a if b2 – 4ac = 5 b2 – 4ac = 5 – 4ca = 5 – b2 w = t – 3 3y2 a = 5 – b2 –4c div the RHS by 3y2 move b2 to the RHS div the RHS by –4c Literal Equations d. Solve for y if a(x – y) = 10 a(x – y) = 10 expand ax – ay = 10
34. 34. b. Solve for w if 3y2w = t – 3 3y2w = t – 3 c. Solve for a if b2 – 4ac = 5 b2 – 4ac = 5 – 4ca = 5 – b2 w = t – 3 3y2 a = 5 – b2 –4c div the RHS by 3y2 move b2 to the RHS div the RHS by –4c Literal Equations d. Solve for y if a(x – y) = 10 a(x – y) = 10 expand ax – ay = 10 subtract ax
35. 35. b. Solve for w if 3y2w = t – 3 3y2w = t – 3 c. Solve for a if b2 – 4ac = 5 b2 – 4ac = 5 – 4ca = 5 – b2 w = t – 3 3y2 a = 5 – b2 –4c div the RHS by 3y2 move b2 to the RHS div the RHS by –4c Literal Equations d. Solve for y if a(x – y) = 10 a(x – y) = 10 expand ax – ay = 10 subtract ax – ay = 10 – ax
36. 36. b. Solve for w if 3y2w = t – 3 3y2w = t – 3 c. Solve for a if b2 – 4ac = 5 b2 – 4ac = 5 – 4ca = 5 – b2 w = t – 3 3y2 a = 5 – b2 –4c div the RHS by 3y2 move b2 to the RHS div the RHS by –4c Literal Equations d. Solve for y if a(x – y) = 10 a(x – y) = 10 expand ax – ay = 10 subtract ax – ay = 10 – ax div by –a
37. 37. b. Solve for w if 3y2w = t – 3 3y2w = t – 3 c. Solve for a if b2 – 4ac = 5 b2 – 4ac = 5 – 4ca = 5 – b2 w = t – 3 3y2 a = 5 – b2 –4c div the RHS by 3y2 move b2 to the RHS div the RHS by –4c Literal Equations d. Solve for y if a(x – y) = 10 a(x – y) = 10 expand ax – ay = 10 subtract ax – ay = 10 – ax div by –a y = 10 – ax –a
38. 38. Multiply by the LCD to get rid of the denominator then solve. Literal Equations
39. 39. –4 = d 3d + b Multiply by the LCD to get rid of the denominator then solve. Example C. Solve for d if Literal Equations
40. 40. –4 = d 3d + b Multiply by the LCD to get rid of the denominator then solve. multiply by the LCD d– 4 = d 3d + b Example C. Solve for d if Literal Equations
41. 41. –4 = d 3d + b Multiply by the LCD to get rid of the denominator then solve. multiply by the LCD d d – 4 = d 3d + b – 4 = d 3d + b ( ) d Example C. Solve for d if Literal Equations
42. 42. –4 = d 3d + b Multiply by the LCD to get rid of the denominator then solve. multiply by the LCD d d – 4 = d 3d + b – 4 = d 3d + b ( ) d Example C. Solve for d if Literal Equations
43. 43. –4 = d 3d + b Multiply by the LCD to get rid of the denominator then solve. multiply by the LCD d d – 4 = d 3d + b – 4 = d 3d + b ( ) d – 4d = 3d + b Example C. Solve for d if Literal Equations
44. 44. –4 = d 3d + b Multiply by the LCD to get rid of the denominator then solve. multiply by the LCD d d – 4 = d 3d + b – 4 = d 3d + b ( ) d – 4d = 3d + b move –4d and b Example C. Solve for d if Literal Equations
45. 45. –4 = d 3d + b Multiply by the LCD to get rid of the denominator then solve. multiply by the LCD d d – 4 = d 3d + b – 4 = d 3d + b ( ) d – 4d = 3d + b – b = 3d + 4d move –4d and b Example C. Solve for d if Literal Equations
46. 46. –4 = d 3d + b Multiply by the LCD to get rid of the denominator then solve. multiply by the LCD d d – 4 = d 3d + b – 4 = d 3d + b ( ) d – 4d = 3d + b – b = 3d + 4d move –4d and b – b = 7d Example C. Solve for d if Literal Equations
47. 47. –4 = d 3d + b Multiply by the LCD to get rid of the denominator then solve. multiply by the LCD d d – 4 = d 3d + b – 4 = d 3d + b ( ) d – 4d = 3d + b – b = 3d + 4d move –4d and b – b = 7d = d 7 –b Example C. Solve for d if Literal Equations div. by 7
48. 48. Exercise. Solve for the indicated variables. Literal Equations 1. a – b = d – e for b. 2. a – b = d – e for e. 3. 2*b + d = e for b. 4. a*b + d = e for b. 5. (2 + a)*b + d = e for b. 6. 2L + 2W = P for W 7. (3x + 6)y = 5 for y 8. 3x + 6y = 5 for y w = t – 3 613. for t w = t – b a14. for t w =11. for t w =12. for t t 6 6 t w = 3t – b a15. for t 16. (3x + 6)y = 5 for x w = t – 3 6 17. + a for t w = at – b 5 18. for t w = at – b c 19. + d for t 3 = 4t – b t 20. for t 9. 3x + 6xy = 5 for y 10. 3x – (x + 6)y = 5z for y