2.1 One Step Equations

Algebra 1, Mrs. Hall 2015-16

Learning target

• I can solve one step equations in one variable.

The diagram shows the amount of money that each player starts with in a video game. To be fair, each player should have the

same amount of money. What amount of money must be in the chest?

32

515

2 1

3

2

Addition and Subtraction Properties of Equality

• Addition Property of Equality:• Adding the same number to each

side of an equation produces an equivalent equation.

• For any real numbers a, b, and c, if a=b, then a + c = b + c

• Example: x - 3 = 2 x - 3 + 3 = 2 + 3

• Subtraction Property of Equality:

• Subtracting the same number from each side of an equation produces an equivalent equation.

• For any real numbers a, b, and c, if a=b, then a – c = b – c

• Example: x + 3 = 2 x + 3 – 3 = 2 – 3

Solving an Equation

• To solve an equation, you must isolate the variable. You do this by getting the variable with a coefficient of 1 alone on one side of the equation.

• You can isolate a variable using the properties of equality and inverse operations.

• An inverse operation undoes another operation. • Subtraction is the inverse of

addition.• Multiplication is the inverse

of division.

x + 13 = 27

-7 = b + 3

9 = x – 3

Multiplication and Division Properties of Equality

Multiplication Property of Equality • Mutliplying each side of an equation

by the same non-zero number produces an equivalent equation.

• For any real numbers a, b, and c, such that c ≠0, then

• Example:

Division Property of Equality • Dividing each side of an equation

by the same nonzero number produces an equivalent equation.

• For any real numbers a, b, and c, such that c≠0, then

• Example:5x=20

Reciprocals

• The product of a number and it’s reciprocal will always equal 1.

• How do we know?

4x = 12

𝑥4=−3

3t = 30

45𝑚=28

7 𝑥=49

Toucan Example

• Toucans and blue and yellow macaws are both tropical birds. The length of an average toucan is about two-thirds of the length of an average blue and yellow macaw. Toucans are about 24 inches long. What is the length of an average blue and yellow macaw?

L= 36

NOW YOU TRY!Complete worksheet for homework. It will be due at the beginning of class next Tuesday!