Foundations of Algebra Review

Adding and Subtracting: Remember SADS

Same Sign: ADD!! 1 + 3 = 4; (-5) - 10 = -15

Different Sign: SUBTRACT!! (-9) + 4 = -5; 6 - 4 = 2

Multiplying and Dividing: Negative Rules

(+)*(+) = (+); (-)*(-) = (+)

(-)*(+) = (-); (+)*(-) = (-)

Like Terms have the same variable and the same exponent

2x + 5x => 7x

3 + 4n + 7 - 3n => 10 + n

Addition Property of Equality

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

Subtraction Property of Equality

if a = b, then a - c = b - c

Example: x - 6 = 13

x - 6 + 6 = 13 + 6

x = 19

Multiplication Property of Equality

if a = b, then a*c = b*c

Division Property of Equality

if a = b, then

Example: 7n = 84

 $\frac{7n}{7}=\frac{84}{7}$  

n = 12

If necessary, simplify Left and Right sides of equations separately by combining like terms (Remember PEMDAS)

Use Properties of Equality to isolate the variable.

Example: 2x + 3 = -7 (Original Equation)

2x + 3 - 3 = -7 - 3 (Subtraction Property of Equality)

2x = -10 (Combine Like Terms)

x = -5 

 $13=3x-3+x$  (Distributive Property)

 $13=4x-3$  (Combining Like Terms)

 $13+3=4x-3+3$  (Addition Property of Equality)

 $16=4x$  (Combining Like Terms)

 $\frac{16}{4}=\frac{4x}{4}$  (Division Property of Equality)

 $4=x$  (Simplify)

 $x=4$  (Symmetric Property)