Equations and Inequalities

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Presentation transcript:

Equations and Inequalities

Equations: True or False?

A number sentence is a statement of equality between two numerical expressions. A number sentence is said to be true if both numerical expressions are equal. If both numerical expressions don’t equal the same number, we say the number sentence is false. True and false statements are called truth values. Number Sentences

Determine whether the following number sentences are true or false Determine whether the following number sentences are true or false. Justify your answer. A. 13+4=7+11 B. 1 2 + 5 8 =1.4−0.275 Examples

An algebraic equation is a statement of equality between two expressions. Algebraic equations can be number sentences (when both expressions contain only numbers), but often they contain variables whose values have not been determined. Algebraic Equation

Example Consider the algebraic equation 4 𝑥+2 =4𝑥+8 Are the expressions on each side of the equal sign equivalent? What does this tell you about the numbers we can substitute for 𝑥? Example

Identifying Properties When Solving Equations

Properties of Equality If x is a solution to an equation, then x 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: 𝑖𝑓 𝑎=𝑏, 𝑡ℎ𝑒𝑛 𝑎+𝑐=𝑏+𝑐 𝑎𝑛𝑑 𝑎−𝑐=𝑏−𝑐 If x is a solution to an equation, x will also be a solution to the new equation formed when each side of the original equation is multiplied by the same number. These are the multiplication and division properties of equality: 𝐼𝑓 𝑎=𝑏, 𝑡ℎ𝑒 𝑎∙𝑐=𝑏∙𝑐 𝑎𝑛𝑑 𝑎 𝑐 = 𝑏 𝑐 Properties of Equality

Solving Equations

Justifying Your Answer Use the properties from previous lessons to justify the reason for each step. Distributive Property Associative Property Commutative Property Addition and Subtraction Property of Equality Multiplication and Division Property of Equality Justifying Your Answer

Distributive Property 2𝑥+7=15 Equivalent Equation Statements Reasons 2 𝑥+5 −3=15 Given 2𝑥+10−3=15 Distributive Property 2𝑥+7=15 Equivalent Equation 2𝑥+7−7=15−7 Addition Property of Equality 2𝑥=8 2𝑥 2 = 8 2 Multiplication Property of Equality 𝑥=4