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Solving Multi-Step Equations

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Solving Multi-Step Equations. Lesson 2-3. Combining Like Terms:. A. 5 = 5m – 23 + 2m Original Equation. 5m – 23 + 2m = 5 Symmetric Property. 5m + 2m + – 23 = 5 Commutative Property.

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Solving Multi-Step Equations
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  1. Solving Multi-Step Equations Lesson 2-3

  2. Combining Like Terms: A. 5 = 5m – 23 + 2m Original Equation 5m – 23 + 2m = 5 Symmetric Property 5m + 2m + – 23 = 5 Commutative Property 7m + – 23 = 5 Combine Like Terms 7m + – 23 + 23 = 5 + 23 Undo subtraction by adding 7m = 28 Simplify (substitution property) Undo multiplication by dividing m = 4 Simplify (substitution property)

  3. B.Martha takes her niece and nephew to a concert. She buys T-shirts and bumper stickers for them. The bumper stickers cost $1 each. Martha’s niece wants 1 shirt and 4 bumper stickers, and her nephew wants 2 shirts, but no bumper stickers. If Martha’s total $67, what is the cost of one shirt? Let _______ = cost of one shirt c _________________________ Cost of 1 shirt + 4 bumper stickers + cost of 2 shirts = total spent ___________________________ Commutative property ___________________________ Combine Like Terms ___________________________ Undo the addition ___________________________ Simplify (Substitution property) ___________________________ Undo the multiplication ___________________________ Simplify (Substitution property) c + 4(1) + 2c = 67 c + 2c + 4 = 67 3c+ 4 = 67 3c + 4 – 4 = 67 – 4 3c = 63 c = 21

  4. Complete the practice problems in your notes. You can check you answers on the last slide of the lesson.

  5. Solving an Equation Using the Distributive Property C. –8 (2x – 1) = 36 –8 (2x + –1) = 36 Rewrite the subtraction as adding the opposite. –16x + 8 = 36 Use the distributive property. –16x + 8 – 8 = 36 – 8 Subtract 8 from each side (undo the addition.) –16x = 28 Simplify Divide each side by -16 (undo the multiplication) Simplify

  6. Solving an Equation that Contains Fractions D. Method 1: Get a common denominator 12 is the LCD for 4 and 3 Remember only subtract numerators. Multiply by the reciprocal. Multiply straight across (10 is a numerator). x = 24 Simplify

  7. Solving an Equation that Contains Fractions D1. Method 2: Clear the fractions from the equation Because 12 is the LCD for 4 and 3, multiply both sides by 12. This eliminates fractions. Distributive property 9x – 4x = 120 5x = 120 Combine Like Terms Divide by 5 (undo the multiplication.) x = 24 Simplify

  8. Solving an Equation that Contains Decimals 3.5 – 0.02x = 1.24 _____________________________ Multiply each side by 102 (because there are 2 places behind the decimal) _____________________________ Distributive Property _____________________________ Subtract from each side. _____________________________ Simplify _____________________________ Divide each side by – 2 _____________________________ Simplify (100) (3.5 – 0.02x) = 1.24 (100) 350 – 2x = 124 350 – 350 – 2x = 124 – 350 – 2x = – 226 x = 113

  9. Solutions to practice problems: m = 6 y = 3 One pack of strings is $14. You earn $8 per hour. x = 6 x = 7. b = 8. m = x = 12.55 x = 2