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4.5 Verbal and Algebraic Expressions/Equations

• Addition sum （합） , • more than, plus, increased by, greater than

• Subtraction difference （차） , • minus, less than, decreased by• (4 less than a number x - 4)

• Multiplication product （곱） , • times, multiplied by , of

• Division quotient （몫） , • divided by, ratio

Verbal Expressions

Practice page 157

• An equation （방정식） is formed when an equal sign is placed between two expressions or constant(s) ( 상수 ).

• is means =

• Ten is three plus seven• 10 = 3 + 7

• Practice page 159

4.6 Linear Equations page 158

Page 159

• Solution of an equation – the value(s) of the variable that make the equation true.

• Equivalent equations – equations that have the same solutions(s).

• Inverse operations – operations that undo one another

(addition – subtraction, multiplication – division)

Solving Equations

the solution is a true statement without a variable (nothing like x = 3 as an answer); every value is a solution – There are infinitely many solutions.

2(x+3) = x+x+6, when you solve you get 0=0Any value for x is a solution

Identity （항등식） page 169= Infinitely Many Solutions 무수히　많은　해

2x=2x+1, when you solve you get a false statement, 0=1When you get a false statement there is no solution.

No Solution （해가　없다）page 169

Steps: • Simplify both sides of the equation• Do opposite of variable on the right side with

addition or subtraction• Do opposite of constant (number) on the left

side with addition or subtraction• Do inverse of the multiplication or division of

the variable to solve

Solving Equations (One method)

Example 7(3 – k) = -3k + 9Simplify each side 21 – 7k = -3k +9 (Distributive

Property)Opposite of variable on the right side

21 – 7k = -3k +9Addition + 3k = +3k .

21 – 4k = 9Opposite of constant on the left side

21 – 4k = 9Subtraction -21 = -21

-4k = -12Opposite of multiplication/division -4 = -4

Divide by -4 k = 3

7(3 – k) = -3k + 9Substitute 3 for k7(3-3) = -3(3) + 90 = -9 + 90 = 0

Check your solutionYou only perform calculations separately on each side (the left side and the right side). Do not add or subtract from one side to the other.If I have an equation 22x-3=1156then my check should be1156 = 1156not any other solution.

1) x + 3 = 2 -3 = -3 x = -1Check -1 + 3 = 2 2 = 2

Practice (One Step Problems)Page 163

(Multi-step) practice page bottom 165

1) distributive property6x – 9 + 2 = 2x + 5

Simplify each side – Combine Like terms 6x – 7 = 2x + 5gather variables to one side by doing inverse

operations and constants to the other side 4x=12last step – inverse operation of multiplication x=3

Check

when checking !!!

check

•Pages 166-168• Solve and CHECK

Homework

Review HomeworkPage 166-168

1) x + 8 =12 -8=-8 x = 4Check 4+8=12 12=12 2)x-4=-6 +4 = +4 x = -2Check -2 – 4 = -6

-6=-6

#20 No Solution