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Unit 1 – First-Degree Equations and Inequalities

Unit 1 – First-Degree Equations and Inequalities. Chapter 1 – Equations and inequalities 1.1 – Expressions and formulas. 1.1 – Expressions and F ormulas. In this section we will review: Using the order of operations to evaluate expressions Using formulas.

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Unit 1 – First-Degree Equations and Inequalities

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  1. Unit 1 – First-Degree Equations and Inequalities Chapter 1 – Equations and inequalities 1.1 – Expressions and formulas

  2. 1.1 – Expressions and Formulas • In this section we will review: • Using the order of operations to evaluate expressions • Using formulas

  3. 1.1 – Real Numbers and Number Operations • Variables – symbols (usually letters) used to represent unknown quantities • Algebraic expressions – Expressions that contain at least one variable • Order of Operations – PEMDAS • Grouping symbols • Powers • Multiply and/or divide from left to right • Add and/or subtract from left to right

  4. 1.1 – Real Numbers and Number Operations • Monomial – An algebraic expression that is a number, a variable, or the product of a number and one or more variables • Ex. 5b, -w, 23, x2, 1/3x3y4 • Constant – monomials that contain no variables • Ex. 23, -1

  5. 1.1 – Real Numbers and Number Operations • Coefficient – Numerical factor of a monomials • Ex. -6 would be the coefficient of -6m. • Degree – Sum of the exponents of its variables • Ex. The degree of 12g7h4 is 7 + 4 or 11 • The degree of a constant is 0 • Power – an expression of the form xn

  6. 1.1 – Real Numbers and Number Operations • Polynomial – Monomial or a sum of monomials • Terms - The monomials that make up a polynomial • Ex. x2 + 2x + x + 1 • Like terms - Terms that have the same variable raised to the same power • Ex. 2x and x in the previous example • x2 + 3x + 1

  7. 1.1 – Real Numbers and Number Operations • Trinomial – A polynomial with three unlike terms • Ex. x2 + 3x + 1 • Binomial – A polynomial with two unlike terms • Ex. xy + z3

  8. 1.1 – Real Numbers and Number Operations • Example 1 • Evaluate the following if x = 2, y = -3, and z = -4 • x + (y – 1)2 • y2 – z(y + z)

  9. 1.1 – Real Numbers and Number Operations Formula – Mathematical sentence that expresses the relationship between certain quantities

  10. 1.1 – Real Numbers and Number Operations • Example 2 • The formula for the area of a trapezoid is • Find the area of the trapezoid shown below 12 in 8 in 48 in

  11. 1.1 – Real Numbers and Number Operations HOMEWORK Page 9 #9 – 19 odd, 21 – 24 all, 32 – 35 all

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