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1.6 Introduction to Solving Equations

1.6 Introduction to Solving Equations. Objectives: Write and solve a linear equation in one variable. Solve a literal equation for a specified variable. Standard: 2.8.11 D Formulate equations to model routine and non-routine problem. An equation is a statement

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1.6 Introduction to Solving Equations

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  1. 1.6 Introduction to Solving Equations Objectives: Write and solve a linear equation in one variable. Solve a literal equation for a specified variable. Standard: 2.8.11 D Formulate equations to model routine and non-routine problem.

  2. An equation is a statement that two expressions are equal. A variable is a symbol that represents many different numbers in a set of numbers. Any value of a variable that makes an equation true is a solution of the equation.

  3. I. Properties of Equality For real numbers a, b, c: • Reflexive Property a = a • Symmetric Property If a = b, then b = a. • Transitive Property If a = b and b = c, then a = c. • Addition Property If a = b, then a + c = b + c. • Subtraction Property If a = b, then a – c = b – c. • Multiplication Property If a = b, then ac = bc. • Division Property If a = b, then a  c = b  c, c  0.

  4. I. Properties of Equality • Tell which Properties of Equality you would use to solve each equation. 1). 52 = -2.7x – 3 Addition Property of Equality Division Property of Equality 2). x = x + 22 2 Multiplication Property of Equality Subtraction Property of Equality

  5. II. Substitution Property If a = b, you may replace a with b in any true statement containing a and the resulting statement will still be true. Ex 1.The relationship between the Celsius temperature, C, and the Fahrenheit temperature, F, is given by F = 9/5 C + 32. Find the Celsius temperature that is equivalent to 86 F. 86 = 9/5C + 32 86 – 32 = 9/5C 54 = 9/5C 30 = C

  6. II. Substitution Property Using the equation given in Example 1, find the Celsius temperature that is equivalent to 122 F. 122 = 9/5C + 32 122 – 32 = 9/5C 90 = 9/5C C = 50

  7. Solve 3x – 8 = 5x – 20. Check your solution by using substitution. 3x – 8 = 5x - 20 -2x – 8 = -20 -2x = -12 X = 6 Check the solution by substitution: 3(6) – 8 = 5 (6) – 20 18 – 8 = 30 – 20 10 = 10

  8. Solve 7 – 6x = 2x –9. Check your solution by using substitution. 7 – 6x = 2x – 9 -8x = -16 X = 2 Check the solution by substitution: 7 – 6(2) = 2(2) – 9 7 – 12 = 4 – 9 -5 = -5

  9. III. An equation may also be solved by graphing!! Type it in y =. Trace to find the point. Ex 1. Solve 3.24x – 4.09 = -0.72x + 3.65 by graphing.

  10. III. An equation may also be solved by graphing!! Type it in y =. Trace to find the point. Ex 2. Solve 2.24x – 6.24 = 4.26x – 8.76 by graphing. Y = 2.24x – 6.24 and y = 4.26x -8.76 X = 1.25

  11. IV. Solve Multi-Step Equations • Distribute • Combine Like Terms • Bring Letters to the Left • Bring Numbers to the Right • Solve for the variable

  12. IV. Solve Multi-Step Equations Ex 1. –2x –7 = 9 -2x = 16 x = -8 Ex 2. 4x + 80 = -6x 10x = -80 x = -8 Ex 3. 3x – 8 = 2x + 2 x – 8 = 2 x = 10

  13. V. Literal Equations An equation that contains two or more variables. Formulas are examples of literal equations. Ex 1. ½ bh = A for b bh = 2A b = 2A/h Ex 2. P = 2l + 2w for w P – 2l = 2w (P-2l)/2 = w

  14. V. Literal Equations Ex 3. A = ½ h(b1 + b2) for b2 2A = h (b1 + b2) (2A)/h = (b1 + b2) b2 = (2A)/h – b1

  15. Writing Activities: Solving Equations 9). Solve 5x – 1 = 3x – 15. Explain each step, and include the Properties of Equality that you used. 10). Explain how you can verify that 3(2x + 5) = 9 + 3x and x = -2 are equivalent equations.

  16. Homework Pg. 49 #12 – 60 even

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