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Introduction to Variables, Algebraic Expressions, and Equations

Section 1.8. Introduction to Variables, Algebraic Expressions, and Equations. A combination of operations on letters (variables) and numbers is called an algebraic expression. Algebraic Expressions 5 + x 6  y 3  y – 4 + x. 4 x means 4  x and xy means x  y.

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Introduction to Variables, Algebraic Expressions, and Equations

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  1. Section 1.8 Introduction to Variables, Algebraic Expressions, and Equations

  2. A combination of operations on letters (variables) and numbers is called an algebraic expression. Algebraic Expressions 5 + x 6y 3y – 4 + x 4xmeans 4x and xymeansxy Martin-Gay, Prealgebra, 5ed

  3. Replacing a variable in an expression by a number and then finding the value of the expression is called evaluating the expression for the variable. Martin-Gay, Prealgebra, 5ed

  4. Evaluating Algebraic Expressions Evaluate x + y for x = 5 and y = 2. Replacexwith5andywith 2 inx + y. x+y = ( ) + ( ) 5 2 = 7 Martin-Gay, Prealgebra, 5ed

  5. Equation Statements like 5 + 2 = 7 are called equations. An equation is of the form expression = expression An equation can be labeled as Equal sign x+ 5 = 9 left side right side

  6. Solving/Solution When an equation contains a variable, deciding which values of the variable make an equation a true statement is called solving an equation for the variable. A solution of an equation is a value for the variable that makes an equation a true statement. Martin-Gay, Prealgebra, 5ed

  7. Solving/Solution ... Determine whether a number is a solution: Is -2 a solution of the equation 2y + 1 = -3? Replace y with -2 in the equation. 2y + 1 = -3 ? 2(-2) + 1 = -3 ? - 4 + 1 = -3 -3 = -3 True Since -3 = -3 is a true statement, -2 is a solution of the equation.

  8. Solving/Solution ... Determine whether a number is a solution: Is 6 a solution of the equation 5x - 1 = 30? Replace x with 6 in the equation. 5x - 1 = 30 ? 5(6) - 1 = 30 ? 30 - 1 = 30 29 = 30 False Since 29 = 30 is a false statement, 6 is not a solution of the equation.

  9. Solving/Solution... To solve an equation, we will use properties of equality to write simpler equations, all equivalent to the original equation, until the final equation has the form x= number or number =x Equivalent equations have the samesolution. The word “number” above represents the solution of the original equation.

  10. Keywords and phrases suggesting addition, subtraction, multiplication, division or equals. Martin-Gay, Prealgebra, 5ed

  11. Translating Word Phrases into Expressions the product of 5 and a number 5x twice a number 2x a number decreased by 3 n- 3 a number increased by 2 z+ 2 four times a number 4w Martin-Gay, Prealgebra, 5ed

  12. Additional Word Phrases into Algebraic Expressions ... x+ 7 three times the sum of a number and 7 3(x+ 7) the quotient of 5 and a number the sum of a number and 7 Martin-Gay, Prealgebra, 5ed

  13. Helpful Hint Remember that order is important when subtracting. Study the order of numbers and variables below. Martin-Gay, Prealgebra, 5ed

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