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Solving equations using addition and subtraction

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Solving equations using addition and subtraction

1. 1. Solving Equations by2-1 Adding or Subtracting Objective Solve one-step equations in one variable by using addition or subtraction.Holt Algebra 1
2. 2. Solving Equations by2-1 Adding or Subtracting Vocabulary equation solution of an equationHolt Algebra 1
3. 3. Solving Equations by2-1 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 Algebra 1
4. 4. Solving Equations by2-1 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 AdditionHolt Algebra 1
5. 5. Solving Equations by2-1 Adding or Subtracting Example 1A: Solving Equations by Using Addition Solve the equation. Check your answer. y – 8 = 24 +8 +8 Since 8 is subtracted from y, add 8 to y = 32 both sides to undo the subtraction. Check y – 8 = 24 To check your solution, 32 – 8 24 substitute 32 for y in the 24 24  original equation.Holt Algebra 1
6. 6. Solving Equations by2-1 Adding or Subtracting Example 1B: Solving Equations by Using Addition Solve the equation. Check your answer. 5 =z– 7 7 16 16 Since is subtracted from z, add 7 to 16 16 + 7 + 7 both sides to undo the subtraction. 16 16 3=z 4 5 =z– 7 Check 16 16 7 To check your solution, 5 3 16 – 4 16 substitute 3 for z in the 4 5 5 original equation. 16 16 Holt Algebra 1
7. 7. Solving Equations by2-1 Adding or Subtracting Check It Out! Example 1a Solve the equation. Check your answer. n – 3.2 = 5.6 + 3.2 + 3.2 Since 3.2 is subtracted from n, add 3.2 n = 8.8 to both sides to undo the subtraction. Check n – 3.2 = 5.6 To check your solution, 8.8 – 3.2 5.6 substitute 8.8 for n in the 5.6 5.6  original equation.Holt Algebra 1
8. 8. Solving Equations by2-1 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 0=k both sides to undo the subtraction. Check –6 = k – 6 To check your solution, –6 0 – 6 substitute 0 for k in the –6 –6  original equation. Link 1Holt Algebra 1
9. 9. Solving Equations by2-1 Adding or SubtractingExample 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 To check your solution, 16 + 17 33 substitute 16 for m in the 33 33  original equation.Holt Algebra 1
10. 10. Solving Equations by2-1 Adding or SubtractingExample 2B: Solving Equations by Using Subtraction Solve the equation. Check your answer. 4.2 = t + 1.8 –1.8 – 1.8 Since 1.8 is added to t, subtract 1.8 from both sides to undo the addition. 2.4 = t Check 4.2 = t + 1.8 To check your solution, 4.2 2.4 + 1.8 substitute 2.4 for t in the 4.2 4.2  original equation.Holt Algebra 1
11. 11. Solving Equations by2-1 Adding or Subtracting Check It Out! Example 2a Solve the equation. Check your answer. d+ 1 =1 2 1 1 – 1 – 1 2 Since 2 is added to d, subtract 2 2 from both sides to undo the addition. d= 1 2 Check d+ 1 =1 To check your solution, 2 1 1 + 1 substitute 2 for d in the 1 2 2 original equation. 1 1Holt Algebra 1
12. 12. Solving Equations by2-1 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 –10 = k both sides to undo the subtraction. Check –5 = k + 5 To check your solution, –5 –10 + 5 substitute –10 for k in the –5 –5  original equation. Link 2Holt Algebra 1
13. 13. Solving Equations by2-1 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 Algebra 1
14. 14. Solving Equations by2-1 Adding or SubtractingExample 3: Solving Equations by Adding the Opposite 2 Solve – 5 + p = – . 11 11 + 5 + 5 5 Since – is added to p, add 5 11 11 11 11 to both sides. 3 p= 11 Check – 5 +p=– 2 11 11 To check your solution, 5 3 – 2 substitute 3 for p in the – + 11 11 11 11 original equation. 2 2 – – 11 11 Holt Algebra 1
15. 15. Solving Equations by2-1 Adding or Subtracting Check It Out! Example 3a Solve –2.3 + m = 7. Check your answer. –2.3 + m = 7 +2.3 + 2.3 Since –2.3 is added to m, m = 9.3 add 2.3 to both sides. Check –2.3 + m = 7 To check your –2.3 + 9.3 7 solution, substitute 9.3 for m in the 7 7 original equation.Holt Algebra 1
16. 16. Solving Equations by2-1 Adding or Subtracting Check It Out! Example 3b 5 Solve – 3 + z = . Check your answer. 4 4 3 +z= 5 – 4 4 3 + 3 Since – 3 is added to z, add 3 + 4 4 4 4 to both sides. z=2 Check – 3 +z= 5 To check your solution, 4 4 substitute 2 for z in the – 3 +2 5 original equation. 4 4 5 5  4 4Holt Algebra 1
17. 17. Solving Equations by2-1 Adding or Subtracting Check It Out! Example 3c Solve –11 + x = 33. Check your answer. –11 + x = 33 +11 +11 Since –11 is added to x, x = 44 add 11 to both sides. Check –11 + x = 33 To check your –11 + 44 33 solution, substitute 44 for x in the original 33 33  equation. Link 3Holt Algebra 1
18. 18. Solving Equations by2-1 Adding or Subtracting Properties of Equality Addition Property of Equality You can add the same number to both WORDS sides of an equation, and the statement will still be true. 3=3 NUMBERS 3+2=3+2 5=5 a=b ALGEBRA a+c=b+cHolt Algebra 1
19. 19. Solving Equations by2-1 Adding or Subtracting Properties of Equality Subtraction Property of Equality You can subtract the same number from WORDS both sides of an equation, and the statement will still be true. 7=7 NUMBERS 7–5=7–5 2=2 a=b ALGEBRA a–c=b–cHolt Algebra 1