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PRESENTATION 13 Simple Equations

PRESENTATION 13 Simple Equations. EQUATIONS. An equation is a mathematical statement of equality between two or more quantities It always contains an equal sign A formula is a particular type of equation that states a mathematical rule. WRITING EQUATIONS.

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PRESENTATION 13 Simple Equations

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  1. PRESENTATION 13 Simple Equations

  2. EQUATIONS • An equation is a mathematical statement of equality between two or more quantities • It always contains an equal sign • A formula is a particular type of equation that states a mathematical rule

  3. WRITING EQUATIONS • The following examples illustrate writing equations from given word statements • A number plus 20 equals 35: • Let n = the number The equation would become: n + 20 = 35 • Four times a number equals 40: • Let x = the number • Four times the number would then be 4x The equation is now: 4x = 40

  4. SUBTRACTION PRINCIPLE OF EQUALITY • The subtraction principle of equality states: • If the same number is subtracted from both sides of an equation, the sides remain equal • The equation remains balanced

  5. SUBTRACTION PRINCIPLE OF EQUALITY • Procedure for solving an equation in which a number is added to the unknown: • Subtract the number that is added to the unknown from both sides of the equation

  6. SUBTRACTION PRINCIPLE OF EQUALITY • Example: Solve x + 5 = 12 for x: • In the equation, the number 5 is added to x so subtract 5 from both sides to solve for x x + 5 = 12 – 5 – 5 x = 7

  7. ADDITION PRINCIPLE OF EQUALITY • The addition principle of equality states: • If the same number is added to both sides of an equation, the sides remain equal • The equation remains balanced

  8. ADDITION PRINCIPLE OF EQUALITY • Procedure for solving an equation in which a number is subtracted from the unknown • Add the number, which is subtracted from the unknown, to both sides of an equation • The equation maintains its balance

  9. ADDITION PRINCIPLE OF EQUALITY • Example: Solve for y: y – 7 = 10 • In the equation, the number 7 is subtracted from y, so add 7 to both sides y – 7 = 10 + 7 + 7 y = 17

  10. DIVISION PRINCIPLE OF EQUALITY • The division principle of equality states: • If both sides of an equation are divided by the same number, the sides remain equal • The equation remains balanced

  11. DIVISION PRINCIPLE OF EQUALITY • Procedure for solving an equation in which the unknown is multiplied by a number: • Divide both sides of the equation by the number that multiplies the unknown • The equation maintains its balance

  12. DIVISION PRINCIPLE OF EQUALITY • Example: Solve for x: 6x = 30 • In the equation, x is multiplied by 6, so divide both sides by 6 x = 5

  13. MULTIPLICATION PRINCIPLE OF EQUALITY • The multiplication principle of equality states: • If both sides of an equation are multiplied by the same number, the sides remain equal • The equation remains balanced

  14. MULTIPLICATION PRINCIPLE OF EQUALITY • Procedure for solving an equation in which the unknown is divided by a number: • Multiply both sides of the equation by the number that divides the unknown • Equation maintains in balance

  15. MULTIPLICATION PRINCIPLE OF EQUALITY • Example: Solve for y: • In the equation, y is divided by 3, so multiply both sides by 3 y = 15

  16. ROOT PRINCIPLE OF EQUALITY • The root principle of equality states: • If the same root of both sides of an equation is taken, the sides remain equal • The equation remains balanced

  17. ROOT PRINCIPLE OF EQUALITY • Procedure for solving an equation in which the unknown is raised to a power: • Extract the root of both sides of the equation that leaves the unknown with an exponent of 1 • Equation maintains in balance

  18. ROOT PRINCIPLE OF EQUALITY • Example: Solve for x: x2 = 25 • In the equation, x is squared, so to solve the equation, extract the square root of both sides x = 5

  19. POWER PRINCIPLE OF EQUALITY • The power principle of equality states: • If both sides of an equation are raised to the same power, the sides remain equal • The equation remains balanced

  20. POWER PRINCIPLE OF EQUALITY • Procedure for solving an equation which contains a root of the unknown: • Raise both sides of the equation to the power that leaves the unknown with an exponent of 1 • Equation maintains in balance

  21. POWER PRINCIPLE OF EQUALITY • Example: Solve for y: • In the equation, y is expressed as a square root, so to solve the equation, square both sides • (√y)2 = (3)2 y = 9

  22. PRACTICAL PROBLEMS • A company’s profit for the second half year is $150,000 greater than the profit for the first half year • The total annual profit is $850,000 • What is the profit for the first half year and the second half of the year?

  23. PRACTICAL PROBLEMS • Let P equal the profit for the first half year • Then P + $150,000 is the profit for the second half year • The sum is $850,000 • Set up an equation: P + P + $150,000 = $850,000 • Sum like terms: 2P + $150,000 = $850,000

  24. PRACTICAL PROBLEMS • Use the subtraction principle of equality and subtract $150,000 from both sides:2P + $150,000 – $150,000 = $850,000 – $150,0002P = $700,000 • Use the division principle of equality and divide both sides by 2 2P ÷ 2 = $700,000 ÷ 2 P = $350,000

  25. PRACTICAL PROBLEMS • The profit for the first half year is $350,000 • The profit for the second half year is $350,000 + $150,000 = $500,000 • Check: Total profit is $350,000 + $500,000, which equals $850,000

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