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Columbus State Community College

Columbus State Community College. Chapter 2 Section 4 Solving Equations Using Division. Solving Equations Using Division. Solve equations using the division property of equality. Simplify equations before using the division property of equality. Solve equations such as – x = 3. a. b. c.

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Columbus State Community College

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  1. Columbus State Community College Chapter 2 Section 4 Solving Equations Using Division

  2. Solving Equations Using Division • Solve equations using the division property of equality. • Simplify equations before using the division property of equality. • Solve equations such as –x = 3.

  3. a b c c = Division Property of Equality Division Property of Equality If a = b, then as long as c is not 0. In other words, you may divide both sides of an equation by the same nonzero number and still keep it balanced.

  4. Equality Principle for Solving an Equation Equality Principle for Solving an Equation As long as you do the same thing to both sides of an equation, the balance is maintained and you still have a true equation. (The only exception is that you cannot divide by 0.)

  5. Using the Division Property of Equality EXAMPLE 1 Using the Division Property of Equality Solve each equation and check each solution. (a) 5n = 30 5n = 30 5 5 n = 6 Solution Check: 5n = 30 5 · 6 = 30 30 = 30 Balance statement

  6. Using the Division Property of Equality EXAMPLE 1 Using the Division Property of Equality Solve each equation and check each solution. (b) 48 = –8x 48 = –8x –8 –8 –6= x Solution Check: 48 = –8x 48 = –8 · –6 48 = 48 Balance statement

  7. 48 = –8x –8 –8 –6= x CAUTION CAUTION Be careful to divide both sides by the same number as the coefficient of the variable term. In Example 1 (b), the coefficient of –8x is –8, so divide both sides by –8. (Do not divide by the opposite of –8, which is 8. Use the opposite only when you’re eliminating a term.) Divide both sides by the coefficient –8.

  8. Simplifying before Solving Equations EXAMPLE 2 Simplifying before Solving Equations Solve each equation and check each solution. (a) 2k – 6k = –14 – 6 2k – 6k = –14 – 6 –4k = –20 –4 –4 k = 5 Solution Check: 2k – 6k = –14 – 6 2(5) – 6(5) = –20 10 – 30 = –20 –20 =–20 Balance statement

  9. Simplifying before Solving Equations EXAMPLE 2 Simplifying before Solving Equations Solve each equation and check each solution. (b) 2– 8 = 11m – 9m 2– 8 = 11m – 9m –6 = 2m 2 2 –3 = m Solution Check: 2– 8 = 11m – 9m –6 = 11(–3) – 9(–3) –6 = –33 + 27 –6 =–6 Balance statement

  10. Solving an Equation of the Type –x = 7 EXAMPLE 3 Solving an Equation of the Type –x = 7 Solve –x = 7 and check the solution. –1x = 7 –1 –1 x = –7 Solution Check: –1 x = 7 –1(–7) = 7 7 = 7 Balance statement

  11. CAUTION CAUTION As the last step in solving an equation, do not leave a negative sign in front of a variable. For example, do not leave –x = –9. Write the understood –1 as the coefficient so that –x = –9 is written as –1x = –9. Then divide both sides by –1 to get x = 9. The solution is 9.

  12. Solving Equations Using Division Chapter 2 Section 4 – Completed Written by John T. Wallace

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