Solving OneStep Equations Section 3 1 2 50

Solving One-Step Equations Section 3. 1 2 -50 even, 53 #17 A mathematician is a device for turning coffee into theorems. ~Paul Erdos

VOCABULARY Inverse Operations • Two operations that undo each other Equivalent Equations • Equations that have the same solutions

Addition and Subtraction Property Addition Property • Adding the same number to each side of an equation produces an equivalent equation • If x-a=b, then x-a+a=b+a, or x=b+a Subtraction Property • Subtracting the same number to each side of an equation produces an equivalent equation • If x+a=b, then x+a-a=b-a, or x=b-a

Examples Add the opposite of positive 7 Add the opposite of -15

Examples

Multiplication & Division Property Multiplication Property • Multiplying each side of an equation by the same nonzero number produces an equivalent equation Division Property • Dividing each side of an equation by the same nonzero number produces an equivalent equation The basic idea is to determine what arithmetic is present and then do the opposite to both sides.

Examples Multiplication present, so divide by the number Leave numbers that don’t work out evenly as improper fractions Division present, so multiply by the number

Examples

Multiplying by the reciprocal Division is the same as • Multiplying by the reciprocal then In many ways, multiplying by the reciprocal is an easier form of the division property of equations

Practical Example Using formulas • Example 6, page 137 • In the 2004 Olympics, Shawn Crawford won the 200 meter dash. His winning time was 19. 79 seconds. Find his average speed to the nearest tenth of a meter per second.

Practical Example Using formulas • Jose’ got a loan of $5000, four years ago. He has finally paid off his loan this month. The total amount of interest he paid was $1600. What was his interest rate per year?

Homework 3. 1 2 -50 even, 53