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 byJillian Scammon
Modified about 1 year ago
© Boardworks Ltd of 27 Equations 1.Equations 2.Using inverse operations 3.Solving equations by transforming both sides 4.Solving an equation with unknowns on both sides
© Boardworks Ltd of 25 © Boardworks Ltd of 27 Equations An equation links an algebraic expression and a number, or two algebraic expressions with an equals sign. For example: x + 7 = 13 is an equation. In an equation the unknown usually has a particular value. Finding the value of the unknown is called solving the equation. x + 7 = 13 x = 6 When we solve an equation we always line up the equals signs.
© Boardworks Ltd of 25 © Boardworks Ltd of 27 Using inverse operations In algebra, letter symbols represent numbers. Rules that apply to numbers in arithmetic apply to letter symbols in algebra. In arithmetic, if = 10, we can use inverse operations to write: 10 – 7 = 3and10 – 3 = 7 In algebra, if a + b = 10, we can use inverse operations to write: 10 – b = a and 10 – a = b a = 10 – b and b = 10 – a or
© Boardworks Ltd of 25 © Boardworks Ltd of 27 b 12 = a Using inverse operations In arithmetic, if 3 × 4 = 12, we can use inverse operations to write: 12 ÷ 4 = 3and12 ÷ 3 = 4 In algebra, if ab = 12, we can use inverse operations to write: and or 12 b = a a = b a = b
© Boardworks Ltd of 25 © Boardworks Ltd of 27 Using inverse operations to solve equations We can use inverse operations to solve simple equations. For example: x + 5 = 13 x = 13 – 5 x = 8 Always check the solution to an equation by substituting the solution back into the original equation. If we substitute x = 8 back into x + 5 = 13 we have = 13
© Boardworks Ltd of 25 © Boardworks Ltd of 27 Using inverse operations to solve equations Solve the following equations using inverse operations. 5 x = 45 x = 45 ÷ 5 x = 9 Check: 5 × 9 = – x = 6 17 = 6 + x 17 – 6 = x Check: 17 – 11 = 6 11 = x x = 11 We always write the letter before the equals sign.
© Boardworks Ltd of 25 © Boardworks Ltd of 27 Using inverse operations to solve equations Solve the following equations using inverse operations. x = 3 × 7 x = 21 Check: 3 x – 4 = 14 3 x = x = 18 Check: 3 × 6 – 4 = 14 x = 18 ÷ 3 x = 6 = 3 7 x 7 21
© Boardworks Ltd of 25 © Boardworks Ltd of 27 4 Solving equations by transforming both sides Solve this equation by transforming both sides in the same way: Add 1 to both sides. Multiply both sides by 4. m = 12 We can check the solution by substituting it back into the original equation: 12 ÷ 4 – 1 = 2 – 1 = 2 m 4 = 3 m +1 ×4
© Boardworks Ltd of 25 © Boardworks Ltd of 27 Solving an equation with unknowns on both sides Let’s solve this equation by transforming both sides of the equation in the same way. 3 n – 11 = 2 n – 3 Start by writing the equation down. −2n−2n −2 n Subtract 2 n from both sides. n – 11 = –3 Always line up the equals signs. +11 Add 11 to both sides. n = 8 This is the solution. We can check the solution by substituting it back into the original equation: 3 8 – 11 =2 8 – 3
Holt Algebra 1 2-Ext Solving Absolute-Value Equations 2-Ext Solving Absolute-Value Equations Holt Algebra 1 Lesson Presentation Lesson Presentation.
8-2: Solving Systems of Equations using Substitution.
Daily Quiz - Simplify the expression, then create your own realistic scenario for the final expression.
Addition and Subtraction Equations Created by Christine Berg Edited by V Hamilton.
Objectives: Understand that algebraic operations follow the same rules as arithmetic operations. Solve simple equations Transform information from words.
1 Section 2.2 introduction an exploration into: Equations with Algebra Tiles Section 2.2 introduction an exploration into: Equations with Algebra Tiles.
Solving Quadratic Equations Using the Zero Product Property.
Copyright©amberpasillas2010. An expression is NOT an equation because it DOES NOT have an equal sign. There are 2 types of expressions Numerical.
8.2 Systems of Linear Equations: Two Equations Containing Two Variables
Variables and Expressions. Vocabulary Variable – A symbol, usually a letter of the alphabet, such as the letter n, that is used to represent a number.
4-4 Equations as Relations Objectives 1. use an equation to determine the range for a given domain 2. graph the solution set for a given domain.
Inverse Operations. How do we undo an operation? If I owe Brandie $1 then how can I get rid of my debt? What math operation would you use to do that?
Chapter 2 Section 3. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. More on Solving Linear Equations Learn and use the four steps for.
Warm up 1.Graph the equation of the line using slope & y-intercept 4x – 2y = 10.
ALGEBRA TILES Expressions and Equations. OBJECTIVES Provide a visual model to help students develop conceptual understanding for variables as unknown.
Chapter 2 Section 4 Solving Equations with variables on both sides- YES!
© Boardworks Ltd of 64 © Boardworks Ltd of 64 A-Level Maths: Core 3 for Edexcel C3.2 Algebra and functions 2 This icon indicates the slide.
Solving Equations with Variables on Both Sides 7-3 Learn to solve equations with variables on both sides of the equal sign.
Holt McDougal Algebra 1 Solving Equations with Variables on Both Sides Solving Equations with Variables on Both Sides Holt Algebra 1 Warm Up Warm Up Lesson.
3-1 Copyright 2010 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Croucher, Introductory Mathematics and Statistics, 5e Chapter 3 Algebra.
Holt Algebra Point-Slope Form Warm Up Find the slope of the line containing each pair of points. 1. (0, 2) and (3, 4) 2. (–2, 8) and (4, 2) 3. (3,
Completing the Square and the Quadratic Formula Objective: To solve quadratic equations by completing the square and using the quadratic formula.
INTRODUCTORY MATHEMATICAL ANALYSIS For Business, Economics, and the Life and Social Sciences 2007 Pearson Education Asia Chapter 0 Review of Algebra.
1-3 Solving Addition and Subtraction Equations Pre-Algebra Warm Up Write an algebraic expression for each word phrase. 1. a number x decreased by 9 2.
LESSON 1.4 EVALUATING EXPRESSIONS. Homework Check & REVIEW Class work and Homework 1.Exercise Pages P. 14 – 16 Q #
Solving Radical Equations. The simplest kind of radical equation is one like this.
Solving Systems of Equations Using Elimination Students will be able to solve systems of equations using elimination.
© Boardworks of 13 Graphing inequalities in two variables.
Solving Inequalities Solving inequalities follows the same procedures as solving equations. There are a few special things to consider with inequalities:
INEQUALITIES Brought To You By- Tutorial Services-The Math Center.
© 2016 SlidePlayer.com Inc. All rights reserved.