1. 2-4 Equations and Their Solutions I CAN determine whether a number is a solution of an equation.

2. 2-4 Equations and Their Solutions equation solution Vocabulary

3. 2-4 Equations and Their Solutions An equation is a mathematical statement that two expressions are equal. You can think of a correct equation as a balanced scale. 3 + 2 5

4. 2-4 Equations and Their Solutions Equations may contain variables. If a value for a variable makes an equation true, that value is a solution of the equation. 12 + 15 27 s + 15 = 27 s = 12s = 10 10 + 15 27 s = 12 is a solution because 12 + 15 = 27. s = 10 is not a solution because 10 + 15  27.

5. 2-4 Equations and Their Solutions The symbol  means “is not equal to.” Reading Math

6. 2-4 Equations and Their Solutions A. Determine whether the given value of the variable is a solution. Example 1: Determining Solutions of Equations b — 447 = 1,203 for b = 1,650 Yes, 1,650 is a solution to b — 447 = 1,203. b — 447 = 1,203 Substitute 1,650 for b. 1,203 = 1,203 ? 1,650 — 447 = 1,203 ? 1,203 Subtract.

7. 2-4 Equations and Their Solutions B. Determine whether the given value of the variable is a solution. Determining Solutions of Equations 27x = 1,485 for x = 54 No, 54 is not a solution to 27x = 1,485. 27x = 1,485 Substitute 54 for x. 1,458 = 1,485 ? 27  54 = 1,485 ? 1,458 1,485 Multiply.

8. 2-4 Equations and Their Solutions A. Determine whether the given value of the variable is a solution. u + 56 = 139 for u = 73 No u + 56 = 139 129 = 139 ? 73 + 56 = 139 ? You Try! Example 1

9. 2-4 Equations and Their Solutions B. Determine whether the given value of the variable is a solution. 45  g = 3 for g = 15 45  g = 3 3 = 3 ? 45  15 = 3 ? You Try! Example 1 Yes

10. 2-4 Equations and Their Solutions An equation has an equal sign, but an expression does not. An equation can be solved, but an expression can only be evaluated or simplified. Reading Math

11. 2-4 Equations and Their Solutions Paulo says that his yard is 19 yards long. Jamie says that Paulo’s yard is 664 inches long. Determine if these two measurements are equal. Example 2: Problem Solving Connection Because 684  664, 19 yards is not equal to 664 inches. Substitute. 684 = 664 ? Multiply. 36  yd = in. 36  19 = 664 ?

12. 2-4 Equations and Their Solutions Anna says that the table is 7 feet long. John says that the table is 84 inches long. Determine if these two measurements are equal. Because 84 = 84, 7 feet is equal to 84 inches. Substitute. 84 = 84 ? 12  7 = 84 ? You Try! Example 2 12  ft = in. Multiply.

13. 2-4 Equations and Their Solutions CAN YOU determine if a number is a solution to an equation ?

14. 2-4 Equations and Their Solutions Determine whether the given value of each variable is a solution. 1. 85 = 13x for x = 5 2. w + 38 = 210 for w = 172 3. 8y = 88 for y = 11 4. 16 = w  6 for w = 98 Lesson Quiz no yes no 5. The local pizza shop charged Kylee $172 for 21 medium pizzas. The price of a medium pizza is $8. Determine whether Kylee paid the correct amount of money. (Hint: $8 pizzas = total cost.)

15. 2-4 Equations and Their Solutions HOMEWORK