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Solve Equations: Understanding One-Step and Two-Step Equations in Math

This guide explains how to solve one-step and two-step equations using addition, subtraction, multiplication, and division. It covers various examples, including real-world problems and routine first-degree equations. Learn to isolate the variable 'x' by applying the Golden Rule of balancing equations. Practice solving equations that involve whole numbers and decimals, and enhance your skills in translating word problems into mathematical symbols. Perfect for students and anyone looking to strengthen their algebra skills.

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Solve Equations: Understanding One-Step and Two-Step Equations in Math

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  1. Bell Ringer • Felicia ate one less than four times the number of cookies Araceli ate. If Felicia ate 11 cookies, how many cookies did Araceli eat? 4a – 1 = 11 4a = 12 a = 3 cookies 4a – 1 One less than twice Araceli Twice Araceli

  2. Homework • x = 4 • x = 12 • x = 1 • x = 6 • x = 16/5 or 3 1/5 • x = -3 • x = -20.83 • x = .56 • x = 2 • x = 16 • x = 8 • x = 45/4 or 11 1/4 • X = 5 • X = 10 • X = 3.7 • X = 7.1 • X = -7 • X = 7 • X = -13 • X = -3 • X = 7.8

  3. XEI 202: Solve equations in the form x + a = b, where a and b are whole numbers or decimals XEI 302: Solve one-step equations having integer or decimal answers XEI 403: Solve routine first-degree equations Solving One-Step Equationswith Multiplication and Division

  4. Example: #1 In order to isolate “x”, we must get rid of the 3!!! 3x = 9 9/3 = 3, so x = 3! 3 3 x = 3 Golden Rule: If we divide one side by 3, we must divide the other side by 3! Check: 3 • 3 = 9 Yes!!!!

  5. Example: #2 In order to isolate “x”, we must get rid of the -4!!! -4x = 20 20/-4 = -5, so x = -5! -4 -4 x = -5 We divide both sides by -4!!! Check: -4 • -5 = 20 Yes!!!!

  6. Example: #3 1 x = 5 4 4 1 4 Multiply by the reciprocal! . Follow Golden Rule! . x = 5 4 1 1 5•4 x = 1 x = 20

  7. Example: #4 Reciprocal Do the same!

  8. Your Turn – Multiply & Divide • x = 7 • x = -5 • x = • x = 16 • x = 15 • x = 12 • 5x = 35 • -3x = 15 • -6x = 20 • ½ x = 8 • 2/5 x = 6 • ¼ x = 3

  9. XEI 403: Solve routine first-degree equations XEI 404: Perform straightforward word-to-symbol translations XEI 501: Solve real-world problems using first-degree equations Two-Step Equations

  10. Review… Multiplication & Division 6x = 18 6 6 x = 3 Addition & Subtraction x + 7 = 5 – 7 – 7 x = -2 -5 + x = 12 +5 +5 x = 17 2 5 x = 8 5 2 . 2 5 . 5 2 x = 8 x = 20

  11. Two-Step Equations Step #1: Get rid of all addition and subtraction first! 2x + 9 = 15 To get rid of the +9, you would – 9 on both sides! – 9 – 9 2x = 6 2 2 Step #2: Get rid of all multiplication and division! To get rid of the 2, divide both sides by 2! x = 3 Check: 2(3) + 9 = 15 6 + 9 = 15 15 = 15

  12. Two-Step Equations -5x – 7 = 13 Addition and Subtraction first! + 7 +7 -5x = 20 -5 -5 Multiplication and division second! x = -4 Check: -5(-4) – 7 = 13 20 – 7 = 13 13 = 13

  13. Two-Step Equations 1 5 x + 2 = 8 – 2 – 2 1 5 . 5 1 5 1 . Multiply by the reciprocal! x = 6 x = 6•5 1 x = 30 Check: 1/5(30) + 2 = 8 6 + 2 = 8 8 = 8

  14. Let’s Try These… 1. 5x – 9 = 11 2. -4x + 6 = 22 3. x + 5 = 20 4. x – 7 = 3 5x = 20 -4x = 16 x = 4 x = -4 3 4 1 6 1 6 3 4 x = 10 x = 15 x = 60 x = 20

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