2.1 Equations

Hi class!

This section is about equations, so let's begin with it's definition.

Equation (equality)- a statement that 2 quantities or expressions are equal (indicated by the = sign) involving a variable

Solution (root)- a number that yields a true statement when substituted for the variable.

This is an example of an equation where the variable is x. The solution, or root, of the equation in x is 4. The number 4 satisfies the equation in x. Each step in the equation above are equivalent equations, having exactly the same solutions. To solve the equation, you must find all of the solutions.

Algebraic equation- contains only algebraic expressions (polynomials, rational expressions, etc.).

Conditional equation- numbers in the domains of the expressions that are not solutions.

ex. x+5=7 This is a conditional equation because a number such as x=6 (or others) is not a solution.

Identity- EVERY number in the domains of the expressions in an algebraic equation is a solution.

ex. (2x+1)(2x-1)=2x-1 The solution to this would be x=x.

Linear equation- an equation that can be written in the form ax+b=0, where a does not equal 0.

Also, if ax+b=0, then x= -b/a

Solving linear equation:

5 x - 6 = 3 x - 8

Subtract 3x from both sides, add 6 to both sides, divide both sides by 2. Check your solution by substituting x with -1 in the original equation.

An equation with no solutions:

Division by 0 is not permissible so if you check the equation and the denominator is 0, the equation has no solution.

Extraneous solution (extraneous root)- a possible solution that is not a solution of the given equation.

x=0 is the extraneous solution.

Equation containing rational expressions:

Well that's basically it on equations, nothing we've never learned before.

Megan