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Equation and Inequality Solving: Essential Techniques

Learn how to solve equations and inequalities step-by-step by applying essential properties. Understand operations and their inverses to find solutions accurately.

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Equation and Inequality Solving: Essential Techniques

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  1. 3.2-3.3/6.1-6.2 Solving Equations/ Inequalities

  2. ESSENTIAL PROPERTY OF EQUATIONS/INEQUALITIES: • Whatever you do to one side, you must do to the other.

  3. How do we know what one step operation to perform? • Every operation has an opposite operation to “undo” it

  4. ORIGINAL OPERATION EQUATION “UNDOING” OPERATION SOLUTION ADDITION x+5 = 2 SUBTRACTION x -5 = 2 MULTIPLICATION 5x = 2 DIVISION = 2 Subtraction x = -3 x =7 Addition Division x=10 Multiplication

  5. SOLVING : • Find all values for the variable that make the equation/inequality true • identify what operation is being used with the variable, and what partner operation will undo it. • keep track of negative signs

  6. Examples: • g + 3/4 = -1/8 • A number increased by 5 is equal to 42.

  7. t – 45  13 7 < x – 4 12 + r ≥ 3 14 > t + 11 SOLVING AN INEQUALITY USING ADDITION AND SUBTRACTION: • ·The rules for solving an EQUATION and an INEQUALITY when you are adding or subtracting are the SAME.

  8. Examples: • (2 ¼)g = 1 ½ • The weight of anything on the moon is about one-sixth its weight on Earth. If an astronaut’s suit weighs 33 pounds on the moon, how much does it weigh on the Earth?

  9. Examples: • The original Great Wall of China was 1000 miles long. In the fourteenth century, the wall had to be repaired and was extended. Today the wall is 2500 miles long. How much of the wall was added during the 1300s?

  10. Example 7&8: • Negative eighteen times a number equals –198. • The rectangle is divided into 5 identical squares. If the perimeter of the rectangle is 48, what is the area of each square?

  11. SOLVING AN INEQUALITY USING MULTIPLICATION & DIVISION: inequality • ·The rules for solving an _______________ when you are multiplying or dividing is ________ different, when you are using a ________________________. • The inequality sign must be __________________ when you multiply or divide by a negative only negative number flipped/switched

  12. Solve the following one step inequalities.

  13. Translate and Solve the Inequality: • The sum of a number and 13 is at least 27. • 33 is greater than the difference of a number and 5. • 5 less than a number is greater than 20. • 2 more than a number is less than -5.

  14. Translate and Solve the Inequality: • Sixteen is no more than two times a number • Negative 7 times y is at least 14. • One-fourth of a number is less than –7. • Two-thirds a number is more than -12.

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