Solving Multi-Step Equations PRE-ALGEBRA LESSON 7-2 (For help, go to Lesson 2-3.) Simplify each expression. 1. 2x + 4 + 3x 2. 5y + y 3. 8a – 5a 4. 2 – 4c + 5c 5. 4x + 3 – 2(5 + x) Check Skills You’ll Need 7-2

Solving Multi-Step Equations PRE-ALGEBRA LESSON 7-2 Solutions 1. 2x + 4 + 3x = (2 + 3)x + 4 = 5x + 4 2. 5y + y = 5y + 1y = (5 + 1)y = 6y 3. 8a – 5a = (8 – 5)a = 3a 4. 2 – 4c + 5c = 2 + (–4c + 5c) = 2 + (–4 + 5)c = 2 + c 5. 4x + 3 – 2(5 + x) = 4x + 3 – 10 – 2x = 4x – 2x – 7 = (4 – 2)x – 7 = 2x – 7 7-2

Solving Multi-Step Equations PRE-ALGEBRA LESSON 7-2 In his stamp collection, Jorge has five more than three times as many stamps as Helen. Together they have 41 stamps. Solve the equation s + 3s + 5 = 41. Find the number of stamps each one has. s + 3s + 5 = 41 4s + 5 = 41 Combine like terms. 4s + 5 – 5 = 41 – 5   Subtract 5 from each side. 4s = 36 Simplify. = Divide each side by 4. 4s 4 36 s = 9 Simplify. 7-2

Solving Multi-Step Equations PRE-ALGEBRA LESSON 7-2 (continued) Helen has 9 stamps. Jorge has 3(9) + 5 = 32 stamps. Check   Is the solution reasonable? Helen and Jorge have a total of 41 stamps. Since 9 + 32 = 41, the solution is reasonable. Quick Check 7-2

Solving Multi-Step Equations PRE-ALGEBRA LESSON 7-2 The sum of three consecutive integers is 42. Find the integers. sum of three consecutive integers 42 is Words Let = the least integer. n Then = the second integer, n + 1 and = the third integer. n + 2 + + n n + 1 n + 2 Equation 42 = 7-2

Solving Multi-Step Equations PRE-ALGEBRA LESSON 7-2 (continued) n + (n + 1) + (n + 2) = 42 (n + n + n) + (1 + 2) = 42 Use the Commutative and Associative Properties of Addition to group like terms together. 3n + 3 = 42 Combine like terms. 3n + 3 – 3 = 42 – 3   Subtract 3 from each side. 3n = 39 Simplify. n = 13 Simplify. = Divide each side by 3. 3n 3 39 7-2

Solving Multi-Step Equations PRE-ALGEBRA LESSON 7-2 (continued) If n = 13, then n + 1 = 14, and n + 2 = 15. The three integers are 13, 14, and 15. Check Is the solution reasonable? Yes, because 13 + 14 + 15 = 42. Quick Check 7-2

Solving Multi-Step Equations PRE-ALGEBRA LESSON 7-2 Solve each equation. a. 4(2q – 7) = –4 4(2q – 7) = –4 8q – 28 = –4 Use the Distributive Property. 8q – 28 + 28 = –4 + 28 Add 28 to each side. 8q = 24 Simplify. Divide each side by 8. = 8q 8 24 q = 3 Simplify. 7-2

Solving Multi-Step Equations PRE-ALGEBRA LESSON 7-2 (continued) b.    44 = –5(r – 4) – r 44 = –5(r – 4) – r 44 = –5r + 20 – r Use the Distributive Property. 44 = –6r + 20 Combine like terms. 44 – 20 = –6r + 20 – 20 Subtract 20 from each side. 24 = –6r Simplify. Divide each side by –6. = 24 –6 –6r Quick Check –4 = r Simplify. 7-2