Evaluating Algebraic Expressions 1-7 Solving Equations by Adding or Subtracting Preparation for AF4.0 Students solve simple linear equations and inequalities over the rational numbers. AF1.4 Use algebraic terminology (e.g., variable, equation, term, coefficient, inequality, expression, constant) correctly. California Standards

Evaluating Algebraic Expressions 1-7 Solving Equations by Adding or Subtracting An equation is a mathematical sentence that uses an equal sign to show that two expressions have the same value. All of these are equations = 11r + 6 = 14–24 = x – 7 –100 2 = 50 To solve an equation that contains a variable, find the value of the variable that makes the equation true. This value of the variable is called the solution of the equation.

Evaluating Algebraic Expressions 1-7 Solving Equations by Adding or Subtracting Determine which value of x is a solution of the equation. x – 4 = 13; x = 9, 27, or 17 Check It Out! Example 1 Substitute each value for x in the equation. Substitute 9 for x. 5 = 13 ?  So 9 is not a solution. x – 4 = 13 ? 9 – 4 = 13 ?

Evaluating Algebraic Expressions 1-7 Solving Equations by Adding or Subtracting Determine which value of x is a solution of the equation. x – 4 = 13; x = 9, 27, or 17 Check It Out! Example 1 Continued Substitute each value for x in the equation. Substitute 27 for x. 23 = 13 ?  So 27 is not a solution. x – 4 = 13 ? 27 – 4 = 13 ?

Evaluating Algebraic Expressions 1-7 Solving Equations by Adding or Subtracting Determine which value of x is a solution of the equation. x – 4 = 13; x = 9, 27, or 17 Check It Out! Example 1 Continued Substitute each value for x in the equation. Substitute 17 for x. 13 = 13 ? So 17 is a solution. x – 4 = 13 ? 17 – 4 = 13 ?

Evaluating Algebraic Expressions 1-7 Solving Equations by Adding or Subtracting Adding and subtracting by the same number are inverse operations. Inverse operations “undo” each other. To solve an equation, use inverse operations to isolate the variable. In other words, get the variable alone on one side of the equal sign. The properties of equality allow you to perform inverse operations. These properties show that you can perform the same operation on both sides of an equation.

Evaluating Algebraic Expressions 1-7 Solving Equations by Adding or Subtracting Solve. Additional Example 2A: Solving Equations Using Addition and Subtraction Properties Since 10 is added to n, subtract 10 from both sides to undo the addition n = 18 – n = 8 n = 8 Identity Property of Addition: 0 + n = n. Check 10 + n = 18 ? = = 18 ? To check your solution, substitute 8 for n in the original equation.

Evaluating Algebraic Expressions 1-7 Solving Equations by Adding or Subtracting Solve. Additional Example 2B: Solving Equations Using Addition and Subtraction Properties Since 8 is subtracted from p, add 8 to both sides to undo the subtraction. p – 8 = p + 0 = 17 p = 17 Identity Property of Addition: p + 0 = p. Check p – 8 = 9 ? 17 – 8 = 9 9 = 9 ? To check your solution, substitute 17 for p in the original equation.

Evaluating Algebraic Expressions 1-7 Solving Equations by Adding or Subtracting Solve. Additional Example 2C: Solving Equations Using Addition and Subtraction Properties Since 11 is subtracted from y, add 11 to both sides to undo the subtraction. 22 = y – = y = y Identity Property of Addition: y + 0 = y. Check 22 = y – 11 ? 22 = 33 – = 22 ? To check your solution, substitute 33 for y in the original equation.

Evaluating Algebraic Expressions 1-7 Solving Equations by Adding or Subtracting Solve. Check It Out! Example 2A Since 15 is added to n, subtract 15 from both sides to undo the addition n = 29 – n = 14 n = 14 Identity Property of Addition: 0 + n = n. Check 15 + n = 29 ? = = 29 ? To check your solution, substitute 14 for n in the original equation.

Evaluating Algebraic Expressions 1-7 Solving Equations by Adding or Subtracting Solve. Check It Out! Example 2B Since 6 is subtracted from p, add 6 to both sides to undo the subtraction. p – 6 = p + 0 = 13 p = 13 Identity Property of Addition: p + 0 = p. Check p – 6 = 7 ? 13 – 6 = 7 7 = 7 ? To check your solution, substitute 13 for p in the original equation.

Evaluating Algebraic Expressions 1-7 Solving Equations by Adding or Subtracting Solve. Check It Out! Example 2C Since 23 is subtracted from y, add 23 to both sides to undo the subtraction. 44 = y – = y = y Identity Property of Addition: y + 0 = 0. Check 44 = y – 23 ? 44 = 67 – = 44 ? To check your solution, substitute 67 for y in the original equation.

Evaluating Algebraic Expressions 1-7 Solving Equations by Adding or Subtracting