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7-1 Pre-Algebra Solving Two-Step Equations Objectives: 1. 2. OBJECTIVE 1 Using Properties to Solve Two-Step Equations IMPORTANT !!! Solving Two-Step Equations 1. Undo Addition or Subtraction. 2. Undo Multiplication or Division. EXAMPLE 1 Undoing an Operation Solve each equation. 1. 3n – 6 = 15 STEPS 1. Undo subtraction by adding 6 to each side. 2. Simplify. 3. Undo multiplication by dividing each side by 3. 4. Simplify. 5. Check. 2. 15x + 3 = 48 3. t 4 - 10 = -6 4. b + 13 = 11 3 5. 9g + 11 = 2 6. 5v – 12 = 8 8. 3x – 5 = 10 9. EXAMPLE 2 n + 10 = 7 2 7. 3x + 4 = 10 10. m - 9 = -5 7 Negative Coefficients Solve each equation. 1. 5 – x = 17 STEPS 1. Subtract 5 from each side. 2. Simplify. 3. 0 – x = -x 4. Divide each side by -1. 5. Simplify. 2. -a + 6 = 8 3. -9 – y = -12 7 4. 13 – 6f = 31 OBJECTIVE 2 EXAMPLE 3 Solving Problems with Two-Step Equations Real-World Problem Solving 1. Lynne wants to save $99 to go to Puerto Rico. She saves $45 each week and now has $180. To find how many more weeks w it will take to have $900, solve 180 + 45w = 900. 2. Jacob bought four begonias in 6-in. pots and a $19 fern at a fundraiser. He spent a total of $63. Solve the equation 4p + 19 = 63 to find the price p of each begonia. 3. You borrow $350 to buy a bicycle. You agree to pay $100 the first week, and then $25 each week until the balance is paid off. To find how many weeks w it will take you to pay for the bike, solve 100 + 25w = 350. Pre-Algebra Objectives 7.1 The student should be able…. 1. To solve two-step equations. 2. To use two-step equations to solve problems.