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LT: I can solve equations and problems by writing equations
Entry Task
?
1.4 Solving Equations
Learning Target: I canSolve equations and solve
problems by writing equations
LT: I can solve equations and problems by writing equations
Vocabulary
Equation Solution to an equation Inverse operation Identity Literal equation
LT: I can solve equations and problems by writing equations
●A variable is a letter which represents an unknown number. Any letter can be used as a variable.
●An algebraic expression contains at least one variable. Examples: a, x+5, 3y – 2z
●A verbal expression uses words to translate algebraic expressions. Example: “The sum of a number and 3”
represents “n+3.”
Review of Terms
LT: I can solve equations and problems by writing equations
An equation is a sentence that states that two mathematical expressions are equal.
Example: 2x-16=18
Vocabulary
LT: I can solve equations and problems by writing equations
Properties of Real Numbers
Reflexive Property
a + b = a + b
The same expression is written on both sides of the equal sign.
LT: I can solve equations and problems by writing equations
Properties of Real Numbers
If a = b then b = a
If 4 + 5 = 9 then 9 = 4 + 5
Symmetric Property
LT: I can solve equations and problems by writing equations
Properties of Real Numbers
Transitive Property
If a = b and b = c then a = c
If 3(3) = 9 and 9 = 4 +5, then 3(3) = 4 + 5
LT: I can solve equations and problems by writing equations
Properties of Real Numbers
Substitution Property
If a = b, then a can be replaced by b.
a(3 + 2) = b(5)
LT: I can solve equations and problems by writing equations
Name the property
A. 5(4 + 6) = 20 + 30
B. 5(4 + 6) = 5(10)
C. 5(4 + 6) = 5(4 + 6)
D. If 5(4 + 6) = 5(10) then 5(10) = 5(4 + 6)
E. 5(4 + 6) = 5(6 + 4)
F. If 5(10) = 5(4 + 6) and 5(4 + 6) = 20 + 30 then 5(10) = 20 + 30
a) Distributiveb) Substitutionc) Reflexive
d) Symmetric
e) Commutative
f) Transitive
LT: I can solve equations and problems by writing equations
Steps to Solving Equations
I. Simplify each side of the equation, if needed, by distributing or combining like terms.
II. Move variables to one side of the equation by using the opposite operation of addition or subtraction.
LT: I can solve equations and problems by writing equations
Steps to Solving Equations cont.
III. Isolate the variable by applying the opposite operation to each side.
I. First, use the opposite operation of addition or subtraction. II. Second, use the opposite operation of multiplication or
division.
IV. Check your answer.
LT: I can solve equations and problems by writing equations
Examples “y” is the variable. Add 6 to each side
to isolate the variable.
Now divide both sides by 3.
The answer is 5.
Check the answer by substituting it into the original equation.
3y – 6 = 9 +6 +6 3y = 15 3 3 y = 5
3(5)-6=915 – 6 = 9
LT: I can solve equations and problems by writing equations
Try this. . .
Did you get x = - 4? You were right!
4 8 24x
LT: I can solve equations and problems by writing equations
Solving Equations - let’s practice
1. 3(2a + 25) - 2(a - 1) = 78
2. 4(x - 7) = 2x + 12 + 2x
a =
No sol.
Identity or many solutions
LT: I can solve equations and problems by writing equations
Literal equations
A literal equation is an equation that uses at least two different variables. You can solve literal equations for any of its one variables by using properties
of equality.
LT: I can solve equations and problems by writing equations
Solving Literal Equations
1. Solve: V = πr2h, for h
2. Solve: de - 4f = 5g, for e
h =
e =
LT: I can solve equations and problems by writing equations
Homework
P. 30 #11,13,17,19,23,26,27,29,31,37,39,47,55,57,62
Challenge# 65