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Mastering Algebraic Expressions, Equations, and Inequalities

Explore and simplify algebraic expressions, solve equations, and understand inequalities using order of operations and properties of equality. Learn to evaluate, solve, and graph equations and inequalities.

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Mastering Algebraic Expressions, Equations, and Inequalities

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Presentation Transcript

  1. Expressions, Equations, and Inequalities Chapter 1

  2. 1.3 Algebraic Expressions • Pg. 18-24 • Obj: Learn how to evaluate and simplify algebraic expressions. • A.SSE.1.a

  3. 1.3 Algebraic Expressions • Evaluate – substitute a number for each variable in the expression and then simplify using the order of operations • Term – an expression that is a number, a variable, or the product of a number and one or more variables • Coefficient – the numerical factor of a term • Constant Term – a term with no variables • Like Terms – have the same variables raised to the same powers

  4. 1.4 Solving Equations • Pg. 26-32 • Obj: Learn how to solve equations and solve problems by writing equations. • A.CED.1, A.CED.4

  5. 1.4 Solving Equations • Equation – a statement that two expressions are equal • Solution of an Equation – finding all values of the variable that make the equation true • Inverse Operations – operations that “undo” each other • Identity – an equation that is true for every value of the variable • Literal Equation – an equation that uses at least two different letters as variables

  6. 1.4 Solving Equations • Properties of Equality • Reflexive – a=a • Symmetric – If a=b, then b=a • Transitive – If a=b and b=c, then a=c • Substitution – If a=b, then you can replace a with b and vice versa

  7. 1.4 Solving Equations • Properties of Equality • Addition – If a=b, then a+c=b+c. • Subtraction – If a=b, then a-c=b-c. • Multiplication – If a=b, then a(c)=b(c) • Division – If a=b, then a/c=b/c

  8. 1.5 Solving Inequalities • Pg. 33-40 • Obj: Learn how to solve and graph inequalities and how to write and solve compound inequalities. • A.CED.1

  9. 1.5 Solving Inequalities • Compound Inequality – Two inequalities joined with the words “and” or “or” • Inequality Symbols and Graphing • Greater Than - > - open circle • Greater Than or Equal to - > - closed circle • Less Than - < - open circle • Less Than or Equal to - < - closed circle

  10. 1.5 Solving Inequalities • Properties of Inequalities • Transitive – If a>b and b>c, then a>c • Addition – If a>b, then a+c>b+c • Subtraction – If a>b, then a-c>b-c • Multiplication – If a>b and c>0, then ac>bc • Division – If a>b and c>0, then a/c > b/c

  11. 1.6 Absolute Value Equations and Inequalities • Pg. 41 – 48 • Obj: Learn how to write and solve equations and inequalities involving absolute value. • A.SSE.1.b, A.CED.1

  12. 1.6 Absolute Value Equations and Inequalities • Absolute Value – the distance of a number from zero – always positive • Extraneous Solution – a solution derived from an original equation that is not a solution of the original equation

  13. 1.6 Absolute Value Equations and Inequalities

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