CHAPTER 7 : EQUATIONS, INEQUATIONS, GRAPHING AND ABSOLUTE VALUE
An algebraic equation is a statement that two algebraic expression are equal. Letters involved in these equations are variable or unknowns.
If the equality is true for certain values of unknowns involved in equations, then these equations are called conditional equations.
The values of unknowns of an equation, satisfying that equation, are known as solutions of that equation.
While solving a problem, we first reduce it to an equation then try to find the value of the unknown in the equation; this is known as "solving the equation"
An equation is not altered if we (1) add equal numbers to each side; (2) subtract equal numbers from each side; (3) multiply each side by equal numbers; (4) divide each side by equal numbers.
Solving Simple Equations :
Example Solve x - 2 = 6
Solution : Adding 2 to each side, we have x = 8
Example Solve x + 3 = 5
Solution : Subtracting 3 from each side, we have x = 2
Solution : Multiplying each side by 3, we have x = 15
Example Solve 3x = 6
Solution : Dividing each side by 3, we have x = 2
Example Solve 7x - 2 = 3x + 6
Solution : Adding 2 to each side; 7x = 3x + 8
Subtracting 3x from each side; 4x = 8
Dividing by 4 to each side; x = 2