1. 2.2 – Solving Equations Using Multiplication and Division

2. 2.2 – Solving Equations Using Multiplication and Division
Goal:
- I can solve one step linear equations using multiplication and division.

3. Special Vocab… (from yesterday
Inverse Operations – are operations that undo each other, such as addition and subtraction. Inverse operations help you isolate the variable in an equation.
* Do the opposite to “undo” an equation!
If you are adding TO the variable – then subtract.
If subtracting FROM the variable – then add.
If multiplying TO the variable, then divide!
If dividing the variable BY something, then multiply by the reciprocal!

4. Transformations that Produce Equivalent Equations
Original Equation
Equivalent Equation
Multiply each side of the equation by the same nonzero number.
Divide each side of the equation by the same nonzero number. x 2 _
= 3
x = 6
x 2
x = 3
4x = 12
Divide by 4

5. Properties of Equality
Multiplication Property of Equality – You can multiply both sides of an equation by the same number and the statement will still be true.
Numbers Algebra
6 = a = b
6(3) = 6(3) a(c) = b(c)
18 = 18

6. Properties of Equality
Division Property of Equality – You can divide both sides of an equation by the same nonzero number, and the statement will still be true.
Numbers Algebra
8 = a = b
2 = 2

7. Practice: Solve the Equations

8. Practice: Solve the Equations

9. Solving equations that contain fractions
Survival Tip – remember that dividing is the same as multiplying by the reciprocal…… you may find it easier to multiply by a reciprocal instead of dividing…..

10. Solving equations that contain fractions

11. Weird Stuff sometimes happens……

12. The distance in miles from the airport that a plane should begin descending, divided by 3, equals the planes height above the ground in thousands of feet. If a plane is 10,000 feet above the ground, write and solve an equation to find the distance at which the pilot should begin descending.
- What if a plane began descending 45 miles from the airport? Find out how high the plane was flying when the descent began.

13. NO PROBLEMO! Quick Review
The inverse operation for multiplication is division, and vice versa.
The Properties of Equality are used to isolate the variable on one side of the equation.
NO PROBLEMO!

14. 2.2 Homework
P87, even, 77-88, #100
Algebra Rocks!
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