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Solving Equations A SolutionA value of the variable that makes the equation a true statement
Equations Example: x + 2 = 5 TRUE if x = 3 FALSE if x = anything else The Solution is x = 3
Special Cases Example: x = x + 1 NEVER TRUE No such number existsCalled a contradiction
Special Cases Example: 2x = x + x ALWAYS TRUE True for any numberCalled an identity
Equivalent Equations Have the same solution Example: x + 2 = 5 x – 1 = 2 x + 4 = 7 All have solution x = 3
Addition Principle Adding (or subtracting) the same number to both sides of an equation does not change its solution.
Addition Principle Example: 6 + x = 8 3+6 + x = 3+8 9 + x = 11Are equivalent equations Both have the same solution
Addition Principle Example: 6 + x = 8 -6 -6 x = 2 x = 2 Equivalent equation that shows the solution
Multiplication PrincipleMultiplying (or dividing) same non-zero number to both sides of an equation does not change its solution.
Multiplication PrincipleExample: 6x = 12 3 • 6x = 3 • 12 18x = 36 Are equivalent equations Both have the same solution
Multiplication PrincipleExample: 6x = 12 6x 6 = 12 6 x = 2 Equivalent equation that shows the solution
Multiplication PrincipleAnother Way:
Using Both Principles Usually best to use Addition Principle first.
Using Both Principles Example: 2x – 3 = 7 First add 3: 2x = 10Then 2: x = 5
Solve 7n – 2 = 5n + 6. Example 1: Solving Equations with Variables on Both Sides To collect the variable terms on one side, subtract 5n from both sides.
Identities, Contradictions and Conditional Equations.
Objectives The student will be able to:
Solving Systems Using Elimination
* Collect the like terms 1. 2a = 2a x -2x + 9 = 6x z – – 5z = 2z - 6.
1. solve equations with variables on both sides. 2. solve equations with either infinite solutions or no solution Objectives The student will be able to:
Solving Equations with the Variable on Both Sides Objectives: to solve equations with the variable on both sides.
Solving 2 step equations. Two step equations have addition or subtraction and multiply or divide 3x + 1 = 10 3x + 1 = 10 4y + 2 = 10 4y + 2 = 10 2b +
1.3 Solving Linear Equations
1. solve equations with variables on both sides. 2. solve equations containing grouping symbols. 3.5 Objectives The student will be able to:
Martin-Gay, Beginning Algebra, 5ed Using Both Properties Divide both sides by 3. Example: 3z – 1 = 26 3z = 27 Simplify both sides. z = 9 Simplify.
1. solve equations with variables on both sides. 2. solve equations containing grouping symbols. Objectives The student will be able to:
The student will be able to: solve equations with variables on both sides. Equations with Variables on Both Sides Objectives Designed by Skip Tyler, Varina.
3.6 & 3.7 Solving Simple One Step Inequalities < > < >
Notes 3.4 – SOLVING MULTI-STEP INEQUALITIES
Solve the equation -3v = -21 Multiply or Divide? 1.
Solving Equations. The equations are equivalent If they have the same solution(s)
The Multiplication Principle of Equality 2.3a 1.Solve linear equations using the multiplication principle. 2.Solve linear equations using both the addition.
Follow the same process as solving multi-step equations. Keep in mind that you want your equation to end up looking like: VARIABLE = NUMBER **It doesn’t.
Math 021. An equation is defined as two algebraic expressions separated by an = sign. The solution to an equation is a number that when substituted.
Section 2.2 More about Solving Equations. Objectives Use more than one property of equality to solve equations. Simplify expressions to solve equations.
3.2 Solving Equations by Using Addition and Subtraction Addition Property of Equality –If the same number is added to each side of an equation, the resulting.
1.7 Intro to Solving Equations Objective(s): 1.) to determine whether an equation is true, false, or open 2.)to find solutions sets of an equation 3.)to.
Solving Equations with the Variable on Both Sides
Solving One Step Equations subtract 3 Adding or subtracting the same number from each side of an equation produces an equivalent equation. Addition.
Algebra 1 Chapter 3 Section Solving Inequalities With Variables on Both Sides Some inequalities have variable terms on both sides of the inequality.
Solve Equations with Variables on Both Sides
MCC8.EE.7 a and b: Solving Equations with Variables on Both Sides.
Objective - To solve equations with the variable in both sides.
Identify the number of solutions of an equation
Solving Equations with Variables on Both Sides. Review O Suppose you want to solve -4m m = -3 What would you do as your first step? Explain.
3.3 Solving Multi-Step Equations. A multi-step equation requires more than two steps to solve. To solve a multi-step equation: you may have to simplify.
7.1 Systems of Linear Equations: Two Equations Containing Two Variables.
Jeopardy Solving Equations Add and Subtract Multiply and Divide Multi-Step Variables on each side Grouping Symbols $100 $200 $300 $400 $500 $100 $200.
Lesson 8.1. » A statement where two mathematical expressions are. » Think of an equation as a balance scale or teeter-totter. The left side must always.
Solving Equations by Adding and Subtracting: Vocabulary Solve: To solve an equation mean to find a solution to the equation. Isolate the variable: Get.
1. solve equations with variables on both sides. 2. solve equations containing grouping symbols. SOL: A.4df Objectives The student will be able to: Designed.
Solving Equations with Variables on Both Sides
Step 1: Simplify Both Sides, if possible Distribute Combine like terms Step 2: Move the variable to one side Add or Subtract Like Term Step 3: Solve for.
Solving Equations with variables on both sides of the Equals
Sullivan Algebra and Trigonometry: Section 1.1 Objectives of this Section Solve an Equation in One Variable Solve a Linear Equation Solve Equations That.
Chapter 1 Section 1. Examples: 2 x 2 system 2 x 3 system 3 x 2 system.
Bkevil Solve Equations With Variables on Both Sides.
Write, Interpret and Use Mathematical Expression and Equations.
A.4f Apply these skills to solve practical problems. A.4b Justify steps used in solving equations. Use a graphing calculator to check your solutions.
Sec. 1-5 Day 1 HW pg (16-26 even, 33-36). An identity is an equation that is true for all values of the variable. An equation that is an identity.
Some problems produce equations that have variables on both sides of the equal sign.
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