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**Solving Equations by Multiplying or Dividing**

Multiplication Property of Equality – you can multiply both sides of an equation by the same #, and the statement will still be true. Example: Solve the equation 8x = 32 for x Step 1: write the equation 8x = 32 Step 2: decide what needs to the 8 needs to move be moved to the other side in order to isolate the variable Step 3: perform the opposite operation 8x/8 = 32/8 to move the constant to the other side Step 4: solve/simplify/evaluate x = 4 Step 5: check your work!

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Division Property of Equality – you can divide both sides of an equation by the same nonzero #, and the statement will still be true. Example: Solve the equation n/5 = 7 for n Step 1: write the equation n/5 = 7 Step 2: decide what needs to the 5 needs to move be moved to the other side in order to isolate the variable Step 3: perform the opposite operation (n/5) (5) = (7) (5) to move the constant to the other side Step 4: solve/simplify/evaluate n = 35 Step 5: check your work!

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**Jack has saved $50, which is one-fourth of the amount he **

Example: Jack has saved $50, which is one-fourth of the amount he needs for a school trip. What is the total amount he needs? Step 1: what are they asking for? Total cost of the trip Step 2: what do we know? $50 saved that is only ¼ of the total Step 3: write an equation ¼ times the total cost = $50 ¼ t = 50 Step 4: solve for the variable (¼ t )(1/4)= (50) (1/4) t = 200 Total cost of the trip is $200 Step 5: Now make sure that makes sense!

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**Solving A 2-Step Problem**

Sometimes you may have to do 2 inverse operations to solve for a variable. Example: Solve 3y – 7 = 20 Step 1: write the problem 3y – 7 = 20 Step 2: move the constant to 3y – = the other side Step 3: simplify 3y = 27 Step 4: move the coefficient to (3y) / 3 = (27) / 3 Step 5: simplify/solve y = 9 Step 6: check your work!

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§ 2.2 The Multiplication Property of Equality. Blitzer, Introductory Algebra, 5e – Slide #2 Section 2.2 Properties of Equality PropertyDefinition Addition.

§ 2.2 The Multiplication Property of Equality. Blitzer, Introductory Algebra, 5e – Slide #2 Section 2.2 Properties of Equality PropertyDefinition Addition.

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