OBJECTIVE I will find solutions to equations using division and multiplication.

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Presentation transcript:

OBJECTIVE I will find solutions to equations using division and multiplication.

Vocabulary Review Inverse Operations - two operations that undo each other Examples: Addition and Subtraction; Multiplication and Division

Vocabulary Properties of Equality - transformations used to isolate a variable

Division Property of Equality Dividing each side of an equation by the same nonzero number produces an equivalent equation. If ax = b and a ≠ 0, then or

Multiplication Property of Equality Multiplying each side of an equation by the same nonzero number produces an equivalent equation. If and a ≠ 0, then or x = ab

Solving an Equation Using Division 8x = -104Original Problem Divide each side by 8 x = -13Simplify AnswerThe solution is -13. Check 8x = (-13) = = -104

Guided Practice 1.-9x = 36

Original Problem Divide each side by 8 x = 104Simplify AnswerThe solution is 104. Check Solving an Equation Using Multiplication

Guided Practice 1.

Multiplying Each Side by a Reciprocal Original Equation Multiply by reciprocal Simplify

Guided Practice 1.

Vocabulary Ratio of a to b = Similar Triangles - two triangles with congruent, corresponding angles; all sides are proportional

Similar Triangles A B C D EF Corresponding

Similar Triangles A B C D EF Corresponding x 6 2 3

Writing and Solving an Equation Solar wind travels at a rate of approximately 2 million kilometers per hour. The sun is about 150 million kilometers from Earth. About how long does it take solar wind to reach Earth? Let t be the time (in hours) that it takes solar wind to reach the Earth.

Writing and Solving an Equation SolutionUse the distance formula to solve. Equation d = rtDistance formula = tSubstitute Divide both sides 75 = t AnswerIt takes the solar wind about 75 hours to reach the Earth.

A large stack of tests is divided into three smaller stacks. Each small stack has 22 papers for the number of students in each class. What is the total number of tests to be given to the three classes? Let x be the number of tests in the large stack. Writing and Solving an Equation

Solution Verbal ModelTotal ÷ Number of Stacks = Tests / Stack Equation AnswerThere are a total of 66 tests in the large stack.

Independent Practice 1.-4x = x = -49