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Solving Equations by by Solving Equations 1-2 1-2 Adding or Subtracting Adding or Subtracting Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 1 Algebra 1 Solving Equations by 1-2 Adding or Subtracting Bell Ringer Solve. 1. 2 + 4 Syllabus is due today! Please turn it in the tray 2. 0.50 + (0.25) 0.75 Give the opposite of each number. 2 2 3. 8 –8 4. 3 3 Evaluate each expression for a = 3 and b = 2. 5. a + 5 8 Holt McDougal Algebra 1 6. 12 b 14 Solving Equations by 1-2 Adding or Subtracting Objective Solve one-step equations in one variable by using addition or subtraction. Holt McDougal Algebra 1 Solving Equations by 1-2 Adding or Subtracting Vocabulary equation solution of an equation Holt McDougal Algebra 1 Solving Equations by 1-2 Adding or Subtracting An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true. To find solutions, isolate the variable. A variable is isolated when it appears by itself on one side of an equation, and not at all on the other side. Holt McDougal Algebra 1 Solving Equations by 1-2 Adding or Subtracting Isolate a variable by using inverse operations which "undo" operations on the variable. An equation is like a balanced scale. To keep the balance, perform the same operation on both sides. Inverse Operations Operation Inverse Operation Addition Subtraction Subtraction Holt McDougal Algebra 1 Addition Solving Equations by 1-2 Adding or Subtracting Example 1A: Solving Equations by Using Addition Solve the equation. Check your answer. y – 8 = 24 +8 +8 y = 32 Check Since 8 is subtracted from y, add 8 to both sides to undo the subtraction. y – 8 = 24 32 – 8 24 24 24 Holt McDougal Algebra 1 To check your solution, substitute 32 for y in the original equation. Solving Equations by 1-2 Adding or Subtracting Example 1B: Solving Equations by Using Addition Solve the equation. Check your answer. 16 = m – 9 +9 + 9 Since 9 is subtracted from m, add 9 to both sides to undo the subtraction. 25 = m Check 16 = m – 9 16 25 – 9 16 16 Holt McDougal Algebra 1 To check your solution, substitute 25 for m in the original equation. Solving Equations by 1-2 Adding or Subtracting Check It Out! Example 1a Solve the equation. Check your answer. n – 3.2 = 5.6 + 3.2 + 3.2 n = 8.8 Check Since 3.2 is subtracted from n, add 3.2 to both sides to undo the subtraction. n – 3.2 = 5.6 8.8 – 3.2 5.6 5.6 5.6 Holt McDougal Algebra 1 To check your solution, substitute 8.8 for n in the original equation. Solving Equations by 1-2 Adding or Subtracting Check It Out! Example 1b Solve the equation. Check your answer. –6 = k – 6 +6 + 6 Since 6 is subtracted from k, add 6 to both sides to undo the subtraction. 0=k Check –6 = k – 6 –6 0 – 6 –6 –6 Holt McDougal Algebra 1 To check your solution, substitute 0 for k in the original equation. Solving Equations by 1-2 Adding or Subtracting Example 2A: Solving Equations by Using Subtraction Solve the equation. Check your answer. m + 17 = 33 – 17 –17 Since 17 is added to m, subtract 17 m = 16 from both sides to undo the addition. Check m + 17 = 33 16 + 17 33 33 33 Holt McDougal Algebra 1 To check your solution, substitute 16 for m in the original equation. Solving Equations by 1-2 Adding or Subtracting Example 2B: Solving Equations by Using Subtraction Solve the equation. Check your answer. 4.2 = t + 1.8 –1.8 – 1.8 2.4 = t Check Since 1.8 is added to t, subtract 1.8 from both sides to undo the addition. To check your solution, 4.2 = t + 1.8 4.2 2.4 + 1.8 substitute 2.4 for t in the original equation. 4.2 4.2 Holt McDougal Algebra 1 Solving Equations by 1-2 Adding or Subtracting Check It Out! Example 2a Solve the equation. Check your answer. d+ 1 =1 2 – 1 – 1 2 2 d= 1 Since 1 is added to d, subtract 1 from 2 2 both sides to undo the addition. 2 Check d+ 1 =1 2 1 + 1 2 2 1 Holt McDougal Algebra 1 1 1 To check your solution, substitute 1 for d in the 2 original equation. Solving Equations by 1-2 Adding or Subtracting Check It Out! Example 2b Solve the equation. Check your answer. –5 = k + 5 –5 – 5 Since 5 is added to k, subtract 5 from both sides to undo the subtraction. –10 = k Check –5 = k + 5 –5 –10 + 5 –5 –5 Holt McDougal Algebra 1 To check your solution, substitute –10 for k in the original equation. Solving Equations by 1-2 Adding or Subtracting Remember that subtracting is the same as adding the opposite. When solving equations, you will sometimes find it easier to add an opposite to both sides instead of subtracting. Holt McDougal Algebra 1 Solving Equations by 1-2 Adding or Subtracting Example 3: Solving Equations by Adding the Opposite 2 . Solve – 5 + p = – 11 11 + 5 + 5 11 11 3 p= 11 Check Since – 5 is added to p, add 5 11 11 to both sides. – 5 +p=– 2 11 11 5 3 – 2 – + 11 11 11 2 2 – – 11 11 Holt McDougal Algebra 1 To check your solution, substitute 3 for p in the 11 original equation. Solving Equations by 1-2 Adding or Subtracting Check It Out! Example 3a Solve –2.3 + m = 7. Check your answer. –2.3 + m = 7 +2.3 + 2.3 m = 9.3 Check Since –2.3 is added to m, add 2.3 to both sides. To check your –2.3 + m = 7 solution, substitute –2.3 + 9.3 7 9.3 for m in the 7 7 original equation. Holt McDougal Algebra 1 Solving Equations by 1-2 Adding or Subtracting Check It Out! Example 3b 5 . Check your answer. Solve – 3 + z = 4 4 3 +z= 5 – 4 4 Since – 3 is added to z, add 3 3 3 + 4 + 4 4 4 to both sides. z=2 Check To check your solution, – 3 +z= 5 4 4 substitute 2 for z in the 3 5 original equation. – +2 4 4 5 5 4 4 Holt McDougal Algebra 1 Solving Equations by 1-2 Adding or Subtracting Check It Out! Example 3c Solve –11 + x = 33. Check your answer. –11 + x = 33 +11 +11 x = 44 Check Holt McDougal Algebra 1 Since –11 is added to x, add 11 to both sides. –11 + x = 33 –11 + 44 33 33 33 To check your solution, substitute 44 for x in the original equation. Solving Equations by 1-2 Adding or Subtracting Properties of Equality WORDS Addition Property of Equality You can add the same number to both sides of an equation, and the statement will still be true. NUMBERS ALGEBRA Holt McDougal Algebra 1 3=3 3+2=3+2 5=5 a=b a+c=b+c Solving Equations by 1-2 Adding or Subtracting Properties of Equality WORDS Subtraction Property of Equality You can subtract the same number from both sides of an equation, and the statement will still be true. NUMBERS ALGEBRA Holt McDougal Algebra 1 7=7 7–5=7–5 2=2 a=b a–c=b–c Solving Equations by 1-2 Adding or Subtracting CLASSWORK/HOMEWORK: 1.2 Worksheet Holt McDougal Algebra 1