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Section 2.1 Linear Equations in One Variable Equation Equation- a mathematical expression that states that two (2) quantities are equal ** Use the equal sign (=) ** ex. 2 + 8 = 10 ex. 10 – 5 = 5 Type of Equation Linear Equation in one variable- equation that can be written in the form . . . ax + b = c or ax = b where a, b, c are constants and a 0 ex. 3x + 9 = 0 ex. 7x + 5 = 2x – 9 ex. 4(x – 2)= 6 ex. x = 6 Linear Equation = First degree equation ** First degree because the highest power on the variable is one. ** Solution to a Linear Equation Solution- the value that can be substituted for the unknown variable so the resulting statement is true Solution Set- the set of all solutions Used to show solution set To determine if a value is a solution? 1. Substitute the value in for the unknown variable. 2. Simplify both sides of the equation. 3. Does it make a true statement (both sides of the equation are equal)? • If yes, then the value is a solution. • If no, then the value is not a solution. For example . . . ex. 4 is a solution to 3x – 5 = 7 ex. 2 is not a solution to 5x – 9 = 6 3x – 5 = 7 5x – 9 = 6 3(4) – 5 = 7 5(2) – 9 = 6 12 – 5 = 7 10 – 9 = 6 7 = 7 1 6 True Statement False Statement Determine if the numbers are solutions to the following equations. ex. ½ ; 2y + 5 = 4 ex. 3 ; 4x + 3 = 18 – x How to Solve Linear Equations • Isolate the variable on one side of the equation so that the number that is the solution is on the other side. Typically variable left-hand side solution right-hand side **But it does not matter which side is which ** Think of = sign as a scale that keeps everything balanced * What you do to one side you must do to the other in order to keep the equation balanced * To isolate the variable use Inverse Operations Inverse Operations- Operations that undo each other. • Addition and Subtraction are inverse operations. • Multiplication and Division are inverse operations. Steps To Solve Linear Equations 1. Simplify both sides of the equation as much as possible • Clear Fractions • Combine like terms • Use distributive property – 3(x + 5) 2. Move all variable terms to one side of the equation and all constant terms to the other side of the equation • Variables-left side of equation, Constants-right side of equation • Use addition or subtraction (Do opposite of what is given) 3. Isolate variable (make the coefficient 1) on one side of equation and solution on the other side • Use multiplication or division (Do opposite of what is given) 4. Check that your solution is correct by substituting it back into original equation to see if it makes a true statement (both sides equal the same value) How to remember rules! S A S M D I D U U I M D B L V P T T I L R I D I A P E F C L Y T Y