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 · 3 |
Correct Distributive property |
| |
= 5x + 15 |
Multiplication |
| 2. 7(4 + y) |
= 4 + 7y |
Incorrect Distributive property |
| 7(4 + y) |
= 7 · 4 + 7y |
Correct Distributive property |
| |
= 28 + 7y |
Multiplication |
| 3. 2(7a + 4) – 5 |
= 2(7a) + 2(4) – 2 · 5 |
Incorrect Distributive property |
| 2(7a + 4) – 5 |
= 2(7a) + 2(4) – 5 |
Correct Distributive property |
| |
= 14 a + 8 – 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 |
| t2 - 5t |
t = - 2 |
(-2)2 – 5(-2)
= 4 + 10 = 14 |
| x2 – 5xy + y2 |
x = 3
y = - 4 |
(3)2 – 5(3)(- 4) + (- 4)2
= 9 + 60 + 16 = 85 |
Sequences: Replace n by the given value:
| 