Presentation on theme: "Linear Equations in One Variable"— Presentation transcript:
1Linear Equations in One Variable Section 2.1Linear Equations in One Variable
2** Use the equal sign (=) ** EquationEquation- a mathematical expression that states that two (2) quantities are equal** Use the equal sign (=) **ex = ex. 10 – 5 = 5
3Type of EquationLinear Equation in one variable- equation that can be written in the form . . .ax + b = c or ax = bwhere a, b, c are constants and a 0ex. 3x + 9 = ex. 7x + 5 = 2x – 9ex. 4(x – 2)= ex. x = 6
4Linear Equation = First degree equation ** First degree because the highest power on the variable is one. **
5Solution to a Linear Equation Solution- the value that can be substituted for the unknown variable so the resulting statement is trueSolution Set- the set of all solutionsUsed to show solution set
6To 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.
7For example . . . ex. 4 is a solution to 3x – 5 = 7 3x – 5 = 7 3(4) – 5 = 712 – 5 = 77 = 7True Statementex. 2 is not a solution to 5x – 9 = 65x – 9 = 65(2) – 9 = 610 – 9 = 61 6False Statement
8Determine if the numbers are solutions to the following equations. ex. ½ ; 2y + 5 = 4ex. 3 ; 4x + 3 = 18 – x
9How 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.Typicallyvariable left-hand sidesolution right-hand side**But it does not matter which side is which **
10Think of = sign as a scale that keeps everything balanced * What you do to one side you must do to theother in order to keep the equation balanced *
11To isolate the variable use Inverse Operations Inverse Operations- Operations thatundo each other.Addition and Subtraction are inverse operations.Multiplication and Division are inverse operations.
12Steps To Solve Linear Equations Simplify both sides of the equation as much as possibleClear FractionsCombine like termsUse distributive property3(x + 5)Move all variable terms to one side of the equation and all constant terms to the other side of the equationVariables-left side of equation, Constants-right side of equationUse 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 sideUse 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)
13How to remember rules! S A S M D I M P L F Y D U B T R A C U L T I P Y VDE