Chapter 3 Notes.pptx - 3.5 Absolute Value Equations 3.4...

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3.4 Compound Inequalities 3.3 Linear Inequalities 3.2 Introduction to Problem Solving 3.1 Linear Equations Chapter 3 - Linear Equations 3.5 Absolute Value Equations
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3.4 Compound Inequalities 3.3 Linear Inequalities 3.2 Introduction to Problem Solving 3.1 Linear Equations Chapter 3 - Linear Equations 3.5 Absolute Value Equations
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3.1 Linear Equations Linear Equation in One Variable – written in the form We solve linear equations by finding all values that make the equation true. The set of these values is called a solution set . where a and b are constants and a ≠ 0. Examples of linear equations in one variable are: Each of these equations can be solved for x , therefore, each equation has exactly one solution. Notice that each equation can be written in the slope- intercept form, y = mx + b, where a = m(slope). 0 b ax 2 8 3 10 5 0 1 2 x x x x
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3.1 Linear Equations Linear equations can be solved symbolically, graphically, or numerically . The symbolic solution is always exact, and properties of equality are used to find the solution. Properties of Equality Addition Property of Equality a = b is equivalent to a + c = b + c which means that whatever you add or subtract to one side of the equation must be added or subtracted to the other side of the equation, as indicated with the variable, c . Multiplication Property of Equality a = b is equivalent to ac = bc, c ≠ 0 which means that whatever you multiply or divide to one side of the equation must be multiplied or divided to the other side of the equation, as indicated with the variable, c , as long as c ≠ 0 .
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Solving Linear Equations Remember, the Order of Operations is used to simplify expressions. Consider the following steps when solving linear equations: 1. Use Distributive Property (to clear parenthesis and combine like terms) 2. Use Addition Property (or subtraction) (to get variables on one side of the equation and constants on the other side) 3. Use Multiplication Property (or division) (to isolate the variables on one side of the equation) 4. Check the solution (by substituting it in the original equation) In essence, you are performing the Order of Operations backwards. This is called using Inverse Operations. 3.1 Linear Equations
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Inverse Operations Inverse operations are used to keep an equation balanced when solving. This ensures that both sides of the equal sign have the same weight or value and it gives your equation validity. The inverse of addition is subtraction. The inverse of multiplication is division. The inverse of square is square root. To keep the equation balanced, we must ask ourselves a series of questions: 1. Which variable(s) am I solving for? 2. What operation is the equation currently performing? 3. What inverse operations must be done to solve for the variable(s)?
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