Download 1 Unit 2 Solving Linear Equations

2.1 Find Square Roots and Compare Real Numbers
Objective(s): 1. Find square roots.
Unit 2 Solving Linear Equations
A square garden has an area of 225 square feet. You want to know how much fencing you should buy to go around the garden without measuring. 2. Compare real numbers.
Terms to KNOW
Radical expression
By knowing how to find square roots, you can find the side length and then determine how much fencing you should buy.
radical
radicand
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­ say as "plus or minus"
­ means to take the positive and negative answer
Terms to KNOW
­ the square of a number x is square root of a number x is ­ the ex. the square of 4 is 16
the square root of 4 is 2
perfect square ­ the square root of a number is an integer (no decimals)
Examples
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2.1 Find Square Roots and Compare Real Numbers (continued)
Objective(s): 1. Find square roots.
2. Compare real numbers.
Terms to KNOW
integers­ whole numbers and their opposites
rational numbers­ can be expressed as a fraction
ex. 1, ,
terminating decimals
­ decimals that "terminate" or stop
ex. 1.5, 2.73, 4.0
repeating decimals­ decimals that have repeating #s or blocks of #s
ex. 1.3, 0.6, 2.141414
irrational numbers­ numbers that do not repeat or stop
ex. , ,
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Real Numbers
Rational Numbers
Irrational Numbers
Integers
Whole Numbers
Erase to reveal
Check for Understanding
Classify each number as real, rational, irrational, whole, or/and integer.
1. 5
2. 0.64
3. 4. 1.427427427
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2.2 Solve One­step equations
Terms to KNOW
Objective(s): 1. Solve one­step equations using addition and subtraction.
inverse operations ­ two operations that undo each other
ex. addition and subtraction
Solve: to determine the value of a variable
To solve an equation
you must isolate the variable.
(Get the variable by itself!)
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Check your work by using substitution. Check for Understanding
m­12=7
x+12=3
r+(­2)=5
y+2=0
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Solve x + (­9) = 14 on the left side. Then write how to solve the problem on the right side.
2.2 Solving One­step equations (cont'd)
Objective(s): 1. Solve one­step equations using multiplication and division.
Work
How
a. x+ ­9 =14
a. given equation
b. x + ­9 = 14
+9 +9
b.
c. x = 23
c. Katrina divided her photos into three albums. Each album contains 26 photos. How many photos did Katrina have to begin with?
reciprocal ­ the inverse of a number
examples: reciprocal = reciprocal = reciprocal = 4x = 48
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How would you solve these problems?
­x = 7
­t = 6
­p = ­9
You can solve by multiplying by ­1 or dividing by ­1.
7 = m
­6
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2.3/2.4 Solve multi­step Equations
We would solve 2x ­ 3 = 5 by working backword...
Think
Today's Objective:
PEMDAS
1. Solve a multi­step equation using addition, subtraction, multiplication, and division.
backwards!
SADMEP
How do you wrap a present?
How do you unwrap it?
Work
2x ­ 3 = 5
How
Work
How
t + 21 = 14
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9
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2.5 Solve Equations with Variables on both sides
Objective(s): 1. Solve equations with variables on both sides.
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no solution- when you end up with two numbers on
opposite sides of the equals sign that are not equal
identity- an equation that is true
for every value of the variable
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Explain why 4x+1=4x+3 has no solution.
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