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# 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 t2 - 5t t = - 2 (-2)2 â€“ 5(-2) = 4 + 10 = 14 x2 â€“ 5xy + y2 x = 3 y = - 4 (3)2 â€“ 5(3)(- 4) + (- 4)2 = 9 + 60 + 16 = 85

Sequences: Replace n by the given value: 