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!
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