Linear Equations in One Variable Section 2.1 Linear Equations in One Variable

** Use the equal sign (=) ** 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? Substitute the value in for the unknown variable. Simplify both sides of the equation. 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 3x – 5 = 7 3(4) – 5 = 7 12 – 5 = 7 7 = 7 True Statement ex. 2 is not a solution to 5x – 9 = 6 5x – 9 = 6 5(2) – 9 = 6 10 – 9 = 6 1 6 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 Simplify both sides of the equation as much as possible Clear Fractions Combine like terms Use distributive property 3(x + 5) 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) 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) 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)

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