Solve Linear Equations with Rational Coefficients - Two-Step Equations

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Learn how to solve two-step linear equations with rational number coefficients by using a combination of addition, subtraction, multiplication, and division. Follow step-by-step instructions to isolate the variable and find the solution. Practice expanding expressions using the distributive property and collecting like terms to determine accurate solutions.

  • Linear Equations
  • Two-Step
  • Rational Coefficients
  • Solving Equations
  • Distributive Property
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  1. Solving Two Solving Two- -Step Equations Step Equations M08.B M08.B- -E.3.1.2 E.3.1.2 SOLVE LINEAR EQUATIONS THAT HAVE RATIONAL NUMBER COEFFICIENTS, INCLUDING EQUATIONS WHOSE SOLUTIONS REQUIRE EXPANDING EXPRESSIONS USING THE DISTRIBUTIVE PROPERTY AND COLLECTING LIKE TERMS.

  2. Solve Two-Step Equations Objective: Students will be able to solve two-step equations showing their steps. Solve 2-step equations using a combination of the four operations: oAddition oSubtraction oMultiplication oDivision

  3. Use two steps to solve equations Use two steps to solve equations This is an equation where you will need more than one step to solve the equation. How can you tell? 2x 5 = 17

  4. Use two steps to solve equations Use two steps to solve equations This is an equation where you will need more than one step to solve the equation. How can you tell? 2x 5 = 17 There is more than one operation in the equation: multiplication and subtraction.

  5. Use two steps to solve equations Use two steps to solve equations 2x 5 = 17 Our first task is to isolate the term with the variable. So, that means we want 2x by itself. How do we do that?

  6. Use two steps to solve equations Use two steps to solve equations We need to add 5 to both sides of the equation. 2x 5 = 17 + 5 +5 (add the number that is subtracted from the variable) 2x = 22

  7. Use two steps to solve equations Use two steps to solve equations Now we have this simple equation. You know what to do! 2x = 22 2 2 x = 11 Check the solution.

  8. Use two steps to solve equations Use two steps to solve equations Check the solution. Start with the original equation. 2x 5 = 17 Substitute the solution in for the variable. 2(11) 5 = 17

  9. Use two steps to solve equations Use two steps to solve equations Continue checking using order of operations. 2(11) 5 = 17 22 5 = 17 17 = 17 This shows the answer is correct!

  10. Use two steps to solve equations Use two steps to solve equations Try one on your own. 5y + 7 = -28 original equation What do you do first? Type your answer in the chat.

  11. Use two steps to solve equations Use two steps to solve equations 5y + 7 = -28 First, subtract 7 from both sides of the equation. (You want to isolate the 5y.) 5y + 7 = -28 7 7 5y = -35 What happens now?

  12. Use two steps to solve equations Use two steps to solve equations What now? To isolate the y, divide both sides by 5. 5y = -35 5 5 y = -7 Now check the solution!

  13. Use two steps to solve equations Use two steps to solve equations Start with the original equation and substitute the solution in for the variable. Simplify. 5y + 7 = -28 5(-7) + 7 = -28 -35 + 7 = -28 -28 = -28 The solution is correct!

  14. Use two steps to solve equations Use two steps to solve equations Let s try another. 9 + m 5 = 11 How do we start? Type your answer in the chat.

  15. Use two steps to solve equations Use two steps to solve equations 9 + m 5 = 11 How do we start? Right! Isolate the term with the variable, so subtract 9 from both sides of the equation.

  16. Use two steps to solve equations Use two steps to solve equations 9 + m 5 = 11 9 9 m 5 = 2 Now what happens?

  17. Use two steps to solve equations Use two steps to solve equations 5 m 5 = 2 5 m = 10 Check the solution. 9 + m 5 = 11 9 + 10 5 = 11 9 + 2 = 11 11 = 11 The solution is correct!

  18. Review solving two-step equations Solve each equation. Show all steps including the check. 1. 3x 5 = 19 2. ? 5 + 6 = -4 3. 6 + 3 = -7 4. 8 + 4f = -16 6. ? 5. -7 + 5n = 23 9 3 = -14

  19. Review solving two-step equations Answers. 1.3x 5 = 19 + 5 + 5 3x = 24 3 3 x = 8 3 8 5 = 19 24 5 = 19 19 = 19 correct *3x 5 = 19

  20. Review solving two-step equations Answers. 2. ? ? 5 + 6 = -4 50 5 + 6 = -4 -10 + 6 = -4 5 + 6 = -4 6 6 * ? 5 = -10 5 ? 5 = -10 5 -4 = -4 correct y = -50

  21. Review solving two-step equations Answers. 3. 6 + 3 = -7 3 3 * 6 + 3 = -7 60 6 + 3 = -7 -6 6 = -10 -6 -10 + 3 = -7 h = 60 -7 = -7 correct

  22. Review solving two-step equations Answers. 4. 8 + 4f = -16 8 4f = -24 4 4 f = -6 * 8 + 4f = -16 8 + 4(-6) = -16 8 + -24 = -16 -16 = -16 It is correct! 8

  23. Review solving two-step equations Answers. 5. 7 + 5n = 37 7 5n = 30 * 7 + 5n = 37 7 + 5 6 = 37 7 + 30 = 37 7 37= 37 5 5 n = 6

  24. Review solving two-step equations Answers. 6. ? * ? 9 3 = -14 99 9 3 = -14 -11 3 = -14 -14 = -14 9 3 = -14 +3 +3 9 ? 9 = -11 9 y = -99

  25. Solving tricky two Solving tricky two- -step Sometimes there are other pieces of information we need to consider when solving equations. Example 1: How do we start this problem? -6 + 4y = 18 step equations equations

  26. Solving tricky two-step equations Example 1: How do we start this problem? -6 + 4y = 18 What do you think? (We know we want to isolate the 4y.)

  27. Solving tricky two-step equations Example 1: How do we start this problem? -6 + 4y = 18 We need to add 6 to both sides of the equation. It looks like we should start by subtracting, but the 6 is negative. So to eliminate it we need to add 6. (You could subtract -6, but that is the same as adding 6.)

  28. Solving tricky two-step equations Solve example 1. -6 + 4y = 18 +6 +6 4y = 24 4 4 y = 6 * -6 + 4y = 18 -6 + 4(6) = 18 -6 + 24 = 18 18 = 18

  29. Solving tricky two-step equations Example 2: What should you do first? 7 3g = 22 Write what you think in the chat. Your answer should include an operation and which term you are using.

  30. Solving tricky two-step equations Example 2: What should you do first? 7 3g = 22 oYou need to subtract 7 from both sides of the equation. (The 7 is not being subtracted from 3g.) oThen, you need to be sure you keep the minus sign with the 3g when you bring it down to the next step.

  31. Solving tricky two-step equations Solve example 2: 7 3g = 22 7 7 -3g = 15 (Be sure you bring the sign with the 3g.) -3 -3 g = -5

  32. Solving tricky two-step equations Check example 2: 7 3g = 22 7 3(-5) = 22 7 -15 = 22 7 + 15 = 22 22 = 22 correct

  33. Review solving tricky two-step equations Solve. Show your steps including the check. 2. 6 ? 7= 4 1. 3x (-5) = 35 3. 12 = -3m 6 4. 5 7m = 54 (Do not rewrite this equation.)

  34. Review solving tricky two-step equations Solve. Show your steps including the check. 6. ? 5. -7 + 5n = 23 9 3 = -14 8. 6 ? 7= 2 7. 26 = -6n 4

  35. Review solving tricky two-step equations Answers. 1. 3x (-5) = 35 3x + 5 = 35 * 3x (-5) = 35 3(10) (-5) = 35 5 5 30 + 5 = 35 3x = 30 35 = 35 3 3 x = 10

  36. Review solving tricky two-step equations answers 2. 6 ? 7= 4 * 6 ? 7= 4 6 70 6 6 -? 7 = -10 -7 -? 7 = -10 -7 -4 = -4 y = 70 7 = -4 6 10 = -4

  37. Review solving tricky two-step equations answers 3. 12 = -3m 6 +6 +6 18 = -3m 12 = 18 6 -3 -3 -6 = m * 12 = -3m 6 12 = -3(-6) 6 12 = 12

  38. Review solving tricky two-step equations answers 4. 5 7m = 54 5 5 -7m = 49 -7 -7 m = -7 * 5 7m = 54 5 7(-7) = 54 5 -49 = 54 5 + 49 = 54 54 = 54

  39. Review solving tricky two-step equations Answer. * -7 + 5 6 = 23 -7 + 30 = 23 -7 + 5n = 23 5. -7 + 5n = 23 +7 +7 5n = 30 23 = 23 5 5 n = 6

  40. Review solving tricky two-step equations 6. ? * ? 9 3 = -14 +3 +3 9 ? 9 3 = -14 99 9 3 = -14 -11 3 = -14 -11 + -3 = -14 -14 = -14 9 = -11 9 y = -99

  41. Review solving tricky two-step equations * 26 = -6n 4 26 = -6 -5 4 26 = 30 4 26 = 26 7. 26 = -6n 4 +4 +4 30 = -6n -6 -6 -5 = n

  42. Review solving tricky two-step equations 8. 6 ? * 6 ? 7= 2 7= 2 7= 2 6 8 = -2 -2 = -2 6 6 -? -7 -? 6 56 7= 8 7= 8 -7 y = 56

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