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1.8

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

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1.8

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

  2. Algebraic Expressions A combination of operations on letters (variables) and numbers is called an algebraic expression. Algebraic Expressions 5 + x 6y 3y – 4 + x 4x means 4x and xy means xy

  3. Algebraic Expressions Replacing a variable in an expression by a number and then finding the value of the expression is called evaluatingtheexpressionfor the variable.

  4. Evaluating Algebraic Expressions Evaluate x + y for x = 5 and y = 2. Replace xwith 5 and y with 2 in x + y. x + y= ( ) + ( ) 5 2 = 7

  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. Solutions 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.

  7. Solutions 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. Solutions 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. Solutions 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 same solution. The word “number” above represents the solution of the original equation.

  10. Keywords and Phrases Keywords and phrases suggesting addition, subtraction, multiplication, division or equals.

  11. Translating Word Phrases 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

  12. Additional Word Phrases the sum of a number and 7 x + 7 three times the sum of a number and 7 3(x + 7) the quotient of 5 and a number

  13. Helpful Hint Remember that order is important when subtracting. Study the order of numbers and variables below.

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