Solve Linear Equations - 1 variable; hanlonmath

Associative Property - Multiplication

(ab)c = a(bc)

Identify for Addition

0, a + 0 = a

Identity for Multiplication

1, a(1) = a

Strategy for solving equations/inequalities containing absolute value

1. Isolate the absolute value 2. Rewrite the absolute value equation/inequality using definition 3. Solve the resulting equations/inequalities

Strategy for solving linear equations- 1 variable

1. Transform the equation into ax + b = c format using the Properties of Real Numbers 2. Use the Order of Operations in reverse using the inverse operation to isolate the variable a. If not in ax + b = c, identify who is physically different b. Get rid of it

24 ÷ 4 x 3 =

18

Order of Operations

An agreement- 1. Grouping 2. Exponentials 3. Multiply/Divide 4. Add/Subtract

Write first step for |2x - 3| = 15

If 2x-3 is positive, then 2x - 3 = 15 if 2x-3 is negative, then - (2x - 3) = 15

Multiplication Property of Equality

If a = b, then ac = bc

What happens when you multiply/divide an inequality by a negative number

Reverse the order of the inequality

What is the difference between an algebraic expression and equation

There is no equal sign in an algebraic expression and you evaluate them by computation. An equation has an equal sign and you are solving for a variable

How is Order of Operations related to solving equations

Us the Order of Operations in reverse using opposite operations to isolate the variable

Which do you do first, multiply or divide

Whichever comes first

Commutative Property - Addition

a + b = b + a

Reflexive Property

a = a

Distributive Property

a(b + c) = ab + ac

General Form of Linear Equation - 1 variable

ax + b = c

Write the first step for |2x - 3| > 15

if 2x - 3 is positive, then 2x - 3 > 15 if 2x - 3 is negative, then - (2x - 3) > 15

Addition Property of Equality

if a = b, then a + c = b + c

Symmetric Property

if a = b, then b = a

Define |x|

x, if x≥ 0 |x|= { -x, if x < 0