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Foundations of Algebra

Solving Two-Step Equations. Foundations of Algebra. An equation written in the form Ax + B = C , where two different algebraic operations are being performed on the variable. What is a Two-Step Equation?. 3x – 5 = 16 y/4 + 3 = 12 5n + 4 = 6 n/2 – 6 = 4. Examples of Two-Step Equations.

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Foundations of Algebra

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  1. Solving Two-Step Equations Foundations of Algebra

  2. An equation written in the form Ax + B = C, where two different algebraic operations are being performed on the variable. What is a Two-Step Equation?

  3. 3x – 5 = 16 • y/4 + 3 = 12 • 5n + 4 = 6 • n/2 – 6 = 4 Examples of Two-Step Equations

  4. 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. Steps for Solving Two-Step Equations

  5. Addition  Subtraction Multiplication  Division Opposite Operations

  6. Identify what operations are on the variable side. (Add, Sub, Mult, Div) • “Undo” the operation by using opposite operations. • Whatever you do to one side, you must do to the other side to keep equation balanced. Helpful Hints?

  7. To solve two-step equations, undo the operations by working backwards. Recall the order of operations as you answer these questions. 1) Ask yourself, • What is the first thing we are doing to x? • What is the second thing? To undo these steps, do the opposite operations in opposite order.

  8. Solve the equations by doing the opposite operations in the opposite order. • Add 3 to both sides • Simplify • Clear the fraction -Multiply both sides by 2 • Simplify • Check your answer

  9. Add 1 to both sides • Simplify • Divide both sides by 2 • Simplify • Check your answer 2) Solve 2x - 1 = -3

  10. Add 4 to both sides • Simplify • Clear the fraction -Multiply both sides by 3 • Simplify • Check your answer 3) Solve

  11. 4) Solve 3y – 1 = 8 • y = 3 • y = -3 • y = • y =

  12. 5) Solve • Clear the fraction - Multiply both sides by 2 • Simplify • Add 4 to both sides • Simplify • Check your answer

  13. 6) Solve • d = -7 • d = -19 • d = -17 • d = 17

  14. 7) Solve • Subtract 3 from both sides • Simplify • Clear the fraction – Multiply both sides by -7 • Simplify • Check your answer This one is tricky! Remember to always use the sign in front of the number.

  15. z = -35 • z = -7 • z = 35 • z = 7 8) Solve 5z + 16 = 51

  16. Subtract 1 from both sides • Simplify • Clear the fraction -Multiply both sides by 5 • Simplify • Divide both sides by 3 • Simplify • Check your answer 9) Solve

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

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

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