We think you have liked this presentation. If you wish to download it, please recommend it to your friends in any social system. Share buttons are a little bit lower. Thank you!
Presentation is loading. Please wait.
Published byBreanna Heather
Modified over 4 years ago
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
Solving Equations with Variables on Both Sides
Identify the number of solutions of an equation
Chapter 3: Parallel and Perpendicular Lines
ONE STEP EQUATIONS.
Solve two-step equations.
Objectives The student will be able to:
MULTIPLICATION EQUATIONS 1. SOLVE FOR X 3. WHAT EVER YOU DO TO ONE SIDE YOU HAVE TO DO TO THE OTHER 2. DIVIDE BY THE NUMBER IN FRONT OF THE VARIABLE.
Objective - To solve equations over given replacement sets. Equalities Inequalities = Equals- is the same as Congruent- same size and shape Similar- same.
Some problems produce equations that have variables on both sides of the equal sign.
Solving Linear Equations
Solving Inequalities with variables on both sides of the Sign
Solving Equations with variables on both sides of the Equals
MCC8.EE.7 a and b: Solving Equations with Variables on Both Sides.
3.6 & 3.7 Solving Simple One Step Inequalities < > < >
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.
Solving Equations with the Variable on Both Sides Objectives: to solve equations with the variable on both sides.
HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 Hawkes Learning Systems. All rights reserved. Hawkes Learning Systems: College Algebra.
Bkevil Solve Equations With Variables on Both Sides.
© 2018 SlidePlayer.com Inc. All rights reserved.