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Mastering Two-Step Equations: A Comprehensive Guide to Solving for Variables

This guide provides an overview of two-step equations, defined as equations in the form Ax + B = C, where A, B, and C are constants. Learn how to solve equations like 3x - 5 = 16 and 5n + 4 = 6 through practical steps. The process involves isolating the variable by first undoing addition or subtraction, followed by multiplication or division. Examples and practice problems reinforce your skills in solving equations and checking answers, ensuring you become proficient in handling two-step equations.

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Mastering Two-Step Equations: A Comprehensive Guide to Solving for Variables

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  1. Bell work x - 10 = 4 3 + x = 2 2x = 12 = 5

  2. Solving Two-Step Equations

  3. What is a Two-Step Equation? An equation written in the form Ax + B = Cwhere A, B, and C are numbers.

  4. Examples of Two-Step Equations • 3x – 5 = 16 • + 3 = 12 • 5n + 4 = 6 • – 6 = 4

  5. Steps for solving • Get the variable term by itself. • In other words, do the addition/subtraction first. • Isolate the variable. • In other words, do the multiplication/ division last. *****HINT! Whatever you do to one side of the equation you MUST do to the other side!

  6. Solve for any Addition or Subtraction on the variable side of equation by “undoing” the operation from both sides of the equation. • Solve any Multiplication or Division from variable side of equation by “undoing” the operation from both sides of the equation.

  7. Addition  Subtraction Inverse “undo” Operations Multiplication  Division

  8. Example • 2x + 3 = 7 *Get the variable term alone* -3-3 “undo” addition by subtraction 2 x = 4 *Isolate the variable* 22 “undo” multiplication by division x = 2

  9. Solve 4x – 5 = 15 4x – 5 = 15 +5 +5 (Add 5 to both sides) 4x = 20 (Simplify) 4 4 (Divide both sides by 4) x = 5 (Simplify)

  10. Try These Examples • 2x – 5 = 17 • 3y + 7 = 25 • 5n – 2 = 38 • 12b + 4 = 28

  11. Check your answers!!! • x = 11 • y = 6 • n = 8 • b = 2

  12. Ex. 2: Solve + 4 = 9 + 4 = 9 - 4 - 4 (Subt. 4 from both sides) = 5 (Simplify)  3 = 5  3 (Mult. by 3 on both sides) x = 15 (Simplify)

  13. Try these examples! • – 3 = 8 • + 4 = 9 • – 6 = 2 • + 4 = 5

  14. Check your answers!!! • x = 55 • c = 35 • r = 24 • d = 9

  15. Time to Review! • Keep the equation balanced. • Use inverse operations to “undo” • Follow the rules: • Undo Addition or Subtaction • Undo Multiplication or Division

  16. Practice: 2 step equations worksheet

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