LT: I can solve equations and problems by writing equations

Entry Task

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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