Lesson 2-1: More on Solving Equations

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Presentation transcript:

Lesson 2-1: More on Solving Equations Objective Students will be able to solve equations involving fraction, decimals, and parenthesis. Students will use the zero products property to solve equations.

Solving Equations Steps (tips for solving flowchart) Simplify Collect like terms on one side Solve (UNDO order of operations) Simplifying Methods Combine like terms Distribute (get rid of parenthesis) Clear fractions or decimals

Example 1 : Parenthesis - Distributing Solve. 5(3 + 2x) = 12 – 4(x – 6) Distribute 15 + 10x = 12 – 4x + 24 Simplify #’s 15 + 10x = 36 – 4x Collect variables – left side 15 + 14x = 36 Solve – subtract 15 both sides 14x = 21 Solve – divide 14 both sides

Example 2 : Clearing Fractions Solve. Clear Fraction - Mult. Each side by common denom. Of 14 2 Simplify fractions Solve – subtract 3 each side Solve – divide by 2 each side

Example 3 : Clearing Decimals Solve. 0.5a + 0.75a + 1.2 = 1.45 Clear decimals – multiply by 100 50a + 75a + 120 = 145 Simplify – combine like terms 125a + 120 = 145 Solve – subtract 120 both sides 125a = 25 Solve – divide by 125 both sides a = 0.2

Zero Products Principle a • b = 0 if and only if a = 0 or b = 0 We have to assume either quantity is zero, so… Example 3: Solve (2x – 4)(3x – 15) = 0 Set both quantities equal to zero and solve both 2x – 4 = 0 or 3x - 15 = 0 x = 2 x = 5 If foiled out this is 6x2 - 42x + 60 = 0. A quadratic equation. The solutions are the x-intercepts!!!