2-2 Solving Two-Step Equations Warm Up Solve each equation x = 112. x – 7 = x = 154. Find a common denominator Possible answer: 6 Possible answer: 20

2-2 Solving Two-Step Equations Preparation for 5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. California Standards

2-2 Solving Two-Step Equations equivalent equations Vocabulary

2-2 Solving Two-Step Equations Additional Example 1A: Solving Two-Step Equations Solve 18 = 4a = 4a + 10 First a is multiplied by 4. Then 10 is added. –10 8 = 4a 2 = a Subtract 10 from both sides. 8 = 4a is equivalent to 18 = 4a Since a is multiplied by 4, divide both sides by 4 to undo the multiplication. The solution set is {2}.

2-2 Solving Two-Step Equations Solve the equation. Check your answer. 7.2 = 1.2y 1.5 = 1.2y – 5.7 Check It Out! Example 1b Add 5.7 to both sides. 7.2 = 1.2y is equivalent to 1.5 = 1.2y – 5.7. Since y is multiplied by 1.2, divide both sides by 1.2 to undo the multiplication. The solution set is {6}. First y is multiplied by 1.2. Then 5.7 is subtracted = y 1.5 = 1.2y – 5.7

2-2 Solving Two-Step Equations Solve the equation. Check your answer. Check It Out! Example 1c n = 0 Subtract 2 from each side. Since n is divided by 7, multiply both sides by 7 to undo the division. The solution set is {0}. First n is divided by 7. Then 2 is added. –2 = 0 = 0 is equivalent to + 2 = 2.

2-2 Solving Two-Step Equations Additional Example 2A: Solving Two-Step Equations That Contain Fractions Solve the equation. Method 1 Use fraction operations. Since is subtracted from, add to both sides to undo the subtraction.

2-2 Solving Two-Step Equations Additional Example 2A Continued y = 16 Since y is divided by 8 multiply both sides by 8. Simplify. The solution set is {16}.

2-2 Solving Two-Step Equations Check It Out! Example 2c Solve the equation. Check your answer. Method 1 Use fraction operations. Since is subtracted from, add to both sides to undo the subtraction.

2-2 Solving Two-Step Equations Check It Out! Example 2c Continued Simplify. The solution set is {15}. n = 15 Since n is multiplied by multiply both sides by the reciprocal,.

2-2 Solving Two-Step Equations Check It Out! Example 2c Continued Check To check your solution, substitute 15 for n in the original equation.

2-2 Solving Two-Step Equations Check It Out! Example 3b Lynda has 12 CDs in her collection. She adds the same number of new CDs to her collection each month. After 7 months Lynda has 26 CDs. How many records does Lynda add each month? The answer will be the number of records that Lynda adds each month. Lynda started with 12 records. Lynda adds records each month. At the end of 7 months she had 26 records. Let r represent the number of records added monthly.

2-2 Solving Two-Step Equations Months is total records Solve 3 7r + 12 = 26 –12 7r = 14 r = 2 records a month Since 12 is added to 7r, subtract 12 from both sides to undo the addition. Since r is multiplied by 7, divide both sides by 7 to undo the multiplication. initial records plus 7r7r = Check It Out! Example 3b Continued

2-2 Solving Two-Step Equations Look Back4 Check that the answer is reasonable. The number of records added per month is 2, so if Lynda started with 12 records and added the 2 per month for 7 months, the total number is equal to 26. Check It Out! Example 3b Continued

2-2 Solving Two-Step Equations Lesson Quiz Solve each equation. 1. 4y + 8 = x = –8 5. Nancy bought 5 rolls of color film and 6 rolls of black-and-white film. The 5 rolls of color film cost $15, and Nancy’s total was $39. Write and solve an equation to find the cost of one roll of black-and-white film. 6b + 15 = 39; $4