Linear Equations and Inequalities in One Variable
Example:
Correct the error on the right side of each of the problems.
1. 5(x + 3) 
= 5x + 3 
Incorrect Distributive property 
5(x + 3) 
= 5x + 5 Â· 3 
Correct Distributive property 

= 5x + 15 
Multiplication 
2. 7(4 + y) 
= 4 + 7y 
Incorrect Distributive property 
7(4 + y) 
= 7 Â· 4 + 7y 
Correct Distributive property 

= 28 + 7y 
Multiplication 
3. 2(7a + 4) â€“ 5 
= 2(7a) + 2(4) â€“ 2 Â· 5 
Incorrect Distributive property 
2(7a + 4) â€“ 5 
= 2(7a) + 2(4) â€“ 5 
Correct Distributive property 

= 14 a + 8 â€“ 5 
Multiplication 

= 14a + 3 
Addition 
Replacement Values
The value of an expression is found by replacing a variable with a given number.
Example:
Find the value of the following expressions by replacing a variable with the given number.
Expression 
Value of the Variable

Value of
the Expression 
2x+ 3 
x = 5 
2
(5) + 3 = 13 
t^{2}  5t 
t =  2 
(2)^{2} â€“ 5(2)
= 4 + 10 = 14 
x^{2} â€“ 5xy + y^{2} 
x = 3
y =  4 
(3)^{2} â€“ 5(3)( 4) + ( 4)^{2}
= 9 + 60 + 16 = 85 
Sequences: Replace n by the given value:
