3.2 – Solving Equations Using Multiplication and Division

Goal: - I can solve one step linear equations using multiplication and division.

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!

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. x2x2 _ = 3 x 2 x = 6 4x = 12 Divide by 4 x = 3

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 = 6a = b 6(3) = 6(3) a(c) = b(c) 18 = 18

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. NumbersAlgebra 8 = 8a = b 2 = 2

Practice: Solve the Equations

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 by a fraction.

Solving equations that contain fractions

Weird Stuff sometimes happens……

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.

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.

Homework In your Textbook: Page 190 #’s 1-8 Page 197 #’s 35-43