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Solving Equations

Solving Equations. Back to the Basics!. How to Solve Equations. 1) ALWAYS do the same thing to BOTH sides of the equation!! It doesn’t matter what you do, if you do it to both sides they will still be equal to each other. If you don’t do it to both sides, the equality is gone.

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Solving Equations

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  1. Solving Equations Back to the Basics!

  2. How to Solve Equations 1) ALWAYS do the same thing to BOTH sides of the equation!! It doesn’t matter what you do, if you do it to both sides they will still be equal to each other. If you don’t do it to both sides, the equality is gone. 2) REVERSE the order of operations rules! 3) Continue until the variable that you are solving for is all by itself on one side of the equal sign. 4) CHECK your answer!! Plug your answer back into the original equation to be sure that it works to make an equal statement.

  3. Single step equations Solve for y:2y = 6 Solve for x:6 = x – 2

  4. Single step equations Solve for y:2y = 6 Divide both sides by 2

  5. Single step equations Solve for y:2y = 6 CHECK your answer!! 2(3) = 6 6 = 6 It checks!

  6. Single step equations Solve for x:6 = x – 2 Add 2 to both sides

  7. Single step equations Solve for x:6 = x – 2 CHECK!! 6 = 8 – 2 6 = 6 It checks

  8. Two Step Equations Solve for x:-3x + 4 = 13 Solve for x:2x + 1 = 7

  9. Two Step Equations Solve for x:-3x + 4 = 13 Get the variable by itself!! REVERSE order of operations! That means subtracting 4 from both sides first. Divide both sides by -3

  10. Two Step Equations Solve for x:-3x + 4 = 13 CHECK your answer! It checks

  11. Two Step Equations Solve for x:2x + 1 = 7 Subtract 1 from both sides Divide both sides by 2

  12. Two Step Equations Solve for x:2x + 1 = 7 CHECK your answer! 2(3) + 1 = 7 6 + 1 = 7 7 = 7 It checks!

  13. Distributing Solve for y:-(y + 8) = 2 Solve for x:3(x+5) = 9

  14. Distributing Solve for x:3(x+5) = 9 Distribute First! Subtract 15 from both sides Divide both sides by 3

  15. Distributing Solve for x:3(x+5) = 9 CHECK! 3(-2+5) = 9 3(3) = 9 9 = 9 It checks

  16. Distributing Solve for y:-(y + 8) = 2 Distribute First! Add 8 to both sides Multiply both sides by -1

  17. Distributing Solve for y:-(y + 8) = 2 CHECK!! It checks

  18. Variables on both sides Solve for x:3x + 7 = 2x + 3 Solve for y:6y + 3 = 2y + 2

  19. Variables on both sides Solve for x:3x + 7 = 2x + 3 Get your variables on one side and numbers on the other. Try to keep your variables positive, if possible. Subtract 2x from both sides. Now move the 7 by subtracting 7 from both sides.

  20. Variables on both sides Solve for x:3x + 7 = 2x + 3 CHECK! 3(-4) + 7 = 2(-4) + 3 -12 + 7 = -8 + 3 -5 = -5 It checks!

  21. Variables on both sides Solve for y:6y + 3 = 2y + 2 Subtract 2y from both sides Subtract 3 from both sides Divide both sides by 4

  22. Variables on both sides Solve for y:6y + 3 = 2y + 2 CHECK!! ; it checks.

  23. Lots of variables! Solve for x:4x + 7 – x = 2x + 13 Solve for x:2x + 7 = 7x + 13 – 3x

  24. Lots of variables! Solve for x:4x + 7 – x = 2x + 13 Combine like terms, then isolate all of the variables on one side becomes Move the 2x by subtracting it from both sides. Subtract 7 from both sides to isolate the variable.

  25. Lots of variables! Solve for x:4x + 7 – x = 2x + 13 CHECK! It checks!

  26. Lots of variables! Solve for x:2x + 7 = 7x + 13 – 3x Combine like terms, then isolate all of the variables on one side becomes Move the 2x by subtracting it from both sides. Subtract 13 from both sides to isolate the variable.

  27. Lots of variables! Solve for x:2x + 7 = 7x + 13 – 3x CHECK! 2(-3) + 7 = 7(-3) +13 – 3(-3) -6 + 7 = -21 + 13 +9 1 = -21 + 22 1 = 1 It checks!

  28. Literal Equations Solve for y:2x + y = 7 Solve for b: A = bh

  29. Literal Equations Solve for y:2x + y = 7 Simply isolate the variable you are solving for!! In this case, isolate the y. Subtract 2x from both sides. , or

  30. Literal Equations Solve for y:2x + y = 7 We can still check this!! 2x + (-2x + 7) = 7 2x – 2x + 7 = 7 7 = 7 It checks!!

  31. Literal Equations Solve for b: A = bh Simply isolate the variable you are solving for!! In this case, isolate the b. Divide both sides by h.

  32. Literal Equations Solve for b: A = bh Check!! Plug your answer in for b The h’s cancel, leaving It checks!!

  33. More literal equations Solve for m:y = mx + b Solve for x:y = mx + b

  34. More literal equations Solve for m:y = mx + b Isolate the variable you are solving for In this case, isolate the m. Subtract b from both sides Divide both sides by x.

  35. More literal equations Solve for m:y = mx + b To check, plug your answer for m into the equation It checks!!

  36. More literal equations Solve for x:y = mx + b Isolate the variable you are solving for In this case, isolate the x. Subtract b from both sides Divide both sides by m.

  37. More literal equations Solve for x:y = mx + b To check, plug your answer for x into the equation It checks!!

  38. Using Background Knowledge! Find the value of x 5x – 22 3x+14 What do we know about opposite sides of rectangles?? They are equal!! To find x, simply set the expression for each side equal to the each other and solve for x.

  39. Using Background Knowledge!

  40. Using Background Knowledge What do we know about the angles of triangles? They add up to 1800!! Set the sum of the 3 angles equal to 180 and solve for x. The third angle is 670. 53 x 60

  41. Using Background Knowledge To check, add the three angles and make sure that they actually add up to 180. 53 + 60 + 67 = 180 180 = 180 It checks 53 x 60

  42. Using Background Knowledge What do we know about the angles of triangles? They add up to 1800!! Plug in to find the angles. . The three angles are 240, 460, & 1100. 24 3x+8 x+12

  43. Using Background Knowledge What do we know about the angles of triangles? They add up to 1800!! To check, add the three angles and make sure that they actually add up to 180. 24 + 46 + 110 = 180 180 = 180 It checks 24 3x+8 x+12

  44. Sneak Preview!! To find the sum of the interior angles of ANY polygon, use the formula , where n is the number of sides. Since this figure has 7 sides, the total of its angles will be (7-2)(180). 5(180) = 900. Set the sum of the 7 sides equal to 900 and solve for x. 132 149 142 x 115 136 120

  45. Sneak Preview!! To find the sum of the interior angles of ANY polygon, use the formula , where n is the number of sides. To check, add up all 7 angles and make sure that they total to 900. 132 149 142 x 115 136 120 It checks

  46. Sneak Preview!! To find the sum of the interior angles of ANY polygon, use the formula , where n is the number of sides. 3x-34 This is still a 7 sided figure; it has a sum of 9000. Set the sum of the 7 sides equal to 900 and solve for x. 2x+21 2x-66 2x+49 136 124 x+20

  47. Sneak Preview!! To find the individual angles, plug in 65 for x and solve. 3x-34 To check, add up the 7 sides to be sure that their sum is 900. 161 + 151 + 85 + 179 + 64 + 136 + 124 = 900 900 = 900; it checks!! 2x+21 2x-66 2x+49 136 124 x+20

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