# Consider the statement 4 5 2 7 this is a

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Consider the statement 4 + 5 = 2 + 7 . This is a grammatically correct sentence. Is the sentence true or false? Consider the statement 1 + 3 = 8 + 6 . This statement is also a grammatically correct sentence. Is the sentence true or false? The previous statements are examples of number sentences Ø A number sentence is a statement of equality between two __________________ expressions. Ø A number sentence is said to be true if both numerical expressions are ___________________. Ø If both numerical expressions don’t equal the same number, we say the number sentence is ____________. . Ø True and false statements are called truth values .
Section 2: Equations and Inequalities 30 Let’s Practice! 3. Consider the algebraic equation 6 + 3 = 9 a. What value can we substitute for 6 to make it a true number sentence? b. How many values could we substitute for 6 and have a true number sentence? 4. Consider the algebraic equation 6 + 6 = 6 + 9 . What values could we substitute for 6 to make it a true number sentence? Try It! 5. Complete the following sentences. a. 8 , = 4 is true for _________________________. b. 29 = 9 + 9 is true for _________________________. c. 8 + 67 = 8 + 68 is true for _________________________. A number sentence is an example of an algebraic equation Ø An algebraic equation is a statement of equality between two __________________. Ø Algebraic equations can be number sentences (when both expressions contain only numbers), but often they contain ________________ whose values have not been determined. Consider the algebraic equation 4 6 + 2 = 46 + 8 Are the expressions on each side of the equal sign equivalent? Justify your answer. What does this tell you about the numbers we can substitute for 6 . . . ?
Section 2 – Topic 2 Identifying Properties When Solving Equations The following equations are equivalent. Describe the operation that occurred in the second equation. 1. Which of the following equations have the correct solution? Select all that apply. , BEAT THE TEST! Want some help? You can always ask questions on the Algebra Wall and receive help from other
Section 2: Equations and Inequalities 31 Algebra Wall students, teachers, and Study Experts. You can also help others on the Algebra Wall and earn Karma Points for doing so. Go to AlgebraNation.com to learn more and get started!
Section 2: Equations and Inequalities 32 Let’s Practice! 1. The following equations are equivalent. Determine the property that was used to write the second equation. a. 6 − 5 = 36 + 7 and 6 − 5 + 5 = 36 + 7 + 5 b. 6 = 36 + 12 and 6 − 36 = 36 − 36 + 12 c. −26 = 12 and E,; E, = +, E, If 6 is a solution to an equation, then 6 will also be a solution to the new equation formed when the same number is added to each side of the original equation. These are the addition and subtraction properties of equality Ø If ? = @ , then ? + A = @ + A and ? − A = @ − A. Ø Give examples of this property. If 6 is a solution to an equation, 6 will also be a solution to the new equation formed when each side of the original equation is multiplied by the same number. Properties of Equality .
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