This document provides examples and explanations for writing equations and inequalities from word problems, as well as solving simple equations using mental math. It includes: 1. An explanation of key terms like open sentence, equation, inequality, and solution in the context of algebraic expressions. 2. Two examples showing how to write equations and inequalities from verbal sentences. 3. An explanation of using mental math to solve simple equations by thinking about the relationship between numbers. 4. Guided practice problems for students to write equations/inequalities and solve simple equations mentally. 5. The assignment listed problems from the textbook pages for additional practice.

1. ANSWER 4(6 – y) 50 + 2t, where t is the number of tickets; $68 ANSWER Lesson 1.4, For use with pages 21-26 1. Write an expression for the phrase: 4 times the difference of 6 and a number y. 2. A museum charges $50 for an annual membership and then a reduced price of $2 per ticket. Write an expression to represent the situation. Then find the total cost to join the museum and buy 9 tickets.

2. Write Equations& Inequalities Section 1.4 P. 21 - 27

3. In this section you will learn to translate verbal sentences into equations or inequalities. There are a lot of key vocabulary words so take good notes.

4. Open sentence Contains two algebraic expressions with a symbol that compares them. 2k – 8 = 12 is an open sentence 4 < 8y is an open sentence

5. Equation An open sentence that contains an equal sign (=) 7x + 3 = -25 Inequality An open sentence that contains one of the symbols

6. Solution When you find a number that make the open sentence TRUE, it is called a solution to the equation or inequality. 7x + 3 = -25 The solution is x = -4

7. There is a chart on P. 21 with symbols that you MAY want to put into your notes. Please learn the meaning of these symbols if they are new.

8. EXAMPLE 1 Write equations and inequalities Verbal Sentence Equation or Inequality a. The difference of twice a numberk and8is 12. 2k – 8 = 12 b. The product of 6 and a number n is at least24. 6n ≥ 24 5 ≤ y ≤ 13 c. A number yis no less than 5 and nomore than13.

9. ANSWER P 30 12 > – for Example 1 GUIDED PRACTICE 1. Write an equation or an inequality: The quotient of a number pand 12 is at least30.

10. ? 8 – 2(3) 2 ≤  2 = 2 3 is a solution. 4(3) – 5 6 7 = 6 3is not a solution. X 2(3) + 5 12 11 > 12 3 is not a solution. X 5 + 3(3) 20  14 ≤ 203is a solution. ? ? ? > = = EXAMPLE 2 Check possible solutions Check whether 3 is a solution of the equation or inequality. Substitute Equation/Inequality Conclusion a.8 – 2x = 2 b.4x– 5 =6 c.2z + 5 > 12 d.5 + 3n ≤ 20

11. 45 = 9  5 a d. = 9 5 EXAMPLE 3 Use mental math to solve an equation Equation Solution Check Think a. x + 4 = 10 6 6 + 4 = 10  What number plus 4 equals10? 20 –12 = 8  20minus whatnumber equals8? b. 20 –y = 8 12 c. 6n = 42 6(7) = 42  6times what numberequals42? 7 What number divided by 5 equals 9? 45

12. 40 = 10  7. r = 10 4 4 for Examples 2 and 3 GUIDED PRACTICE Solve the equation using mental math. Equation Solution Check Think 5. m + 6 = 11 5 5 + 6 = 11  What number plus 6 equals11? 5(8) = 40  5times whatnumber equals40? 6. 5x = 40 8 What number dividedby 4 equals 10 40

13. Assignment: P. 24 1-11all, 12-34 evens only