Do Now Determine which numbers in the set are natural, whole, integers, rational and irrational -9, -7/2, 5, 2/3, √2, 0, 1, -4, 2, -11 Evaluate |x + 2|, x < -2 X + 2

P-2 Solving Equations

Equation– a statement that two algebraic expression are equal. Example— 3x – 6 = 18 Solve—find the values of x for which an equation is true (Solutions)

Polynomial Equations –a n x n + a n-1 x n-1 + …. Degree Identity—an equation that is true for every real number in the domain. Example– x 2 – 9 = (x – 3)(x + 3) 2x + 4 = 2(x + 2) x/3x 2 = 1/3x where x ≠ o Conditional equations– an equation that is true for just some (or even none) of the real numbers in the domain Example-- x 2 – 9 =0 x 2 – 6x = -9

Solving Linear Equations After solving, check your solutions by substituting it back into the equation!!! When multiplying or dividing an equation by a variable quantity, it is possible to introduce an extraneous solution that does not satisfy the original equation. Solving Fractional Equations

Quadratic Equations Factoring x 2 – x- 6 = 0 -x 2 + 8x = 12 4x x + 9 = 0

Quadratic Equations Quadratic formula x = -b   b 2 – 4ac 2a x 2 + 8x + 14 = 0 2x 2 - x - 1 = 0

Quadratic Equations Square root principle (extracting the roots) x 2 = 32 (x + 13) 2 = 25

Quadratic Equations Completing the Square x 2 + 2x – 6 = 0 2x 2 + 4x – 8 = 0

4 th power equations x = 0 Regular Trig Stop here on day 2 3x 4 - 6x x 2 = 0

Factor by grouping x 3 – 3x 2 – 3x + 9 = 0 Only ever try when the equation is cubed!!!

Find all solutions…. √5 – x = 3