This document provides examples and explanations for solving equations using mental math. It includes sample equations such as 15 - n = 4 and their step-by-step solutions. Students are guided through additional practice problems solving for variables in equations and determining if a given value satisfies the equation. The document aims to teach students how to set up and solve one-step equations using logic and arithmetic operations.

1. Lesson 1.5 , For use with pages 26-30 Evaluate the expression when x = 11 . 1. 3 x 2 2. 5 x – 17

2. Lesson 1.5 , For use with pages 26-30 Evaluate the expression when x = 11 . 1. 3 x 2 2. 5 x – 17 ANSWER 363 ANSWER 38

3. Lesson 1.5 Equations and Solutions Objective: To be able to write and solve equations using mental math.

4. Equation : mathematical sentence formed by placing an equal sign between two expressions. Solution : of a variable equation is the number that you can substitute for a variable to make the equation true. Solving an equation : finding all the solutions of an equation. Vocabulary

5. EXAMPLE 1 Using Mental Math to Solve Equations Solve the equation using mental math. Write these in your note book and solve them. SOLUTION To solve an equation using mental math, think of the equation as a question. a. 15 – n = 4 a. 15 minus what number equals 4 ? 15 – 11 = 4, so n = 11.

6. EXAMPLE 1 Using Mental Math to Solve Equations Solve the equation using mental math. Write these in your note book and solve them. SOLUTION To solve an equation using mental math, think of the equation as a question. b. 8 x = 32 b. 8 times what number equals 32 ? 8( 4 ) = 32, so x = 4.

7. EXAMPLE 1 Using Mental Math to Solve Equations Solve the equation using mental math. Write these in your note book and solve them. SOLUTION To solve an equation using mental math, think of the equation as a question. c. r 12 = 4 c. What number divided by 12 equals 4 ? 48 12 = 4, so r = 48.

8. GUIDED PRACTICE for Examples 1, 2, and 3 Solve the equation using mental math. SOLUTION To solve an equation using mental math, think of the equation as a question. 1. 5 x = 45 5 times what number equals 45 ? 5(9) = 45, so x = 9.

9. GUIDED PRACTICE for Examples 1, 2, and 3 Solve the equation using mental math. SOLUTION To solve an equation using mental math, think of the equation as a question. 16 plus what number equals 21 ? 16 + 5 = 21, so n = 5. 2. 16 + n = 21

10. GUIDED PRACTICE for Examples 1, 2, and 3 Solve the equation using mental math. SOLUTION To solve an equation using mental math, think of the equation as a question. What number divided by 6 equals 9 ? 54 6 = 9, so r = 54. 3. t 6 = 9

11. GUIDED PRACTICE for Examples 1, 2, and 3 SOLUTION Tell whether the value of the variable is a solution of the equation. y = 8 Substitute for y and then simplify. 4. 88 y = 8 11 8 ≠ 88 8 8 88 y = 8 No, 8 is not a solution. ANSWER

12. GUIDED PRACTICE for Examples 1, 2, and 3 SOLUTION 16 = 16 Substitute for a and then simplify. a + 9 = 16 Tell whether the value of the variable is a solution of the equation. a = 7 ANSWER Yes, 16 is a solution. 7 + 9 16 5. a + 9 = 16

13. GUIDED PRACTICE for Examples 1, 2, and 3 SOLUTION Tell whether the value of the variable is a solution of the equation. n = 2 Substitute for n and then simplify. 7 n = 13 6. 7 n = 13 7(2) 13 14 13 ≠ No, 2 is not a solution. ANSWER

14. Do together: page 29 #45-50

15. Do together: page 29 #45-50 14 + x = 43 x = 29 in.

16. Do together: page 29 #45-50

17. Do together: page 29 #45-50 12f = 3600 f = 300 ft.

18. Do together: page 29 #45-50 5033 + b = 5396 b = 363 lbs.

19. Do together: page 29 #45-50 Substitute 5 for x and evaluate the expression to see that 4(5) = 20.

20. Do together: page 29 #45-50

21. Do together: page 29 #45-50 20 min at x dollars per min equals $25,000; 20x = 25,000; $50,000 If the rate is the same the time is doubled, the total cost is also doubled.

22. Homework Page 28 #1-24