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# Solving Two-Step Equations

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1. Solving Two-Step Equations

2. What is a Two-Step Equation? An equation written in the form Ax + B = C

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

4. Steps for Solving Two-Step Equations PEMDAS in Reverse… • 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.

5. Opposite Operations Addition  Subtraction Multiplication  Division

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

7. Ex. 1: Solve 4x – 5 = 11 4x – 5 = 11 +5 = +5 (Add 5 to both sides) 4x = 16 (Simplify)  4 =  4 (Divide both sides by 4) x = 4 (Simplify)

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

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

10. Ex. 2: Solve x  3 + 4 = 9 x  3 + 4 = 9 - 4 = - 4 (Subtract 4 from both sides) x3 = 5 (Simplify) (x3) 3 = 5  3 (Multiply by 3 on both sides) x = 15 (Simplify)

11. Try these examples! • r3 – 6 = 2 • d9 + 4 = 5 x 5 – 3 = 8 c7 + 4 = 9

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

13. Time to Review! • Make sure your equation is in the form Ax + B = C • Keep the equation balanced. • Use opposite operations to “undo” Follow the rules (PEMDAS in Reverse): • Undo Addition or Subtraction • Undo Multiplication or Division

14. Wait! There’s more…

15. Solving Multi-Step Equations

16. What is a Multi-Step Equation? A multi-step equations takes more than two steps to solve. The same rules for two-step equations apply, but now you have equations that require you to do additional work BEFORE you begin to isolate the variable.

17. Examples of Multi-Step Equations • 8x - 3x - 10 = 20 • 7x + 2(x + 6) = 39 • (3x + 5) = -24

18. Steps for Solving Multi-Step Equations • Start by simplifying one or both sides of the equation. This may require: • Combining like terms • Using the distributive property • Multiplying by a reciprocal • Use inverse operations (PEMDAS in reverse) to isolate the variable.

19. Ex 1: 8x - 3x - 10 = 20 8x – 3x – 10 = 20 Original equation 5x – 10 = 20 Combine like terms +10 = +10 Add 10 to both sides 5x = 30 Simplify 5 = 5 Divide both sides by 5 x = 6 Simplify

20. Ex 2: 7x + 2(x + 6) = 39 7x + 2(x + 6) = 39 Original equation 7x + 2x + 12 = 39 Distributive property 9x + 12 = 39 Combine like terms -12 = -12 Subtract 12 from both sides 9x = 27 Simplify 9 = 9 Divide both sides by 9 x = 3 Simplify

21. Ex 3: (3x + 5) = -24 (3/2)(3x + 5) = -24 Original equation ·(2/3) = ·(2/3) Multiply by reciprocal 3x + 5 = -16 Simplify (-24/1 * 2/3 = -48/3 = -16) -5 = -5 Subtract 5 from both sides 3x = -21 Simplify 3 = 3 Divide both sides by 3 x = -7 Simplify

22. Try these examples! • 5h + 2(11 – h) = -5 • (3/2)(x – 5) = -6 12v + 14 + 10v = 80 3 + 4(z + 5) = 31

23. Check your answers!!! h = -9 x = 1 v = 3 z = 2

24. Homework • TB pp. 144-145 #1, 3, 7, 11, 15, 19, 21, 22, 25, 27, 31, 35, 40 • TB pp. 150-151 #1, 5, 11, 13, 17, 18, 19, 23, 27, 31