Ch. 2 Vocabulary ( continued)

Slides:

Advertisements

Similar presentations

1.3 Solving Equations 1.5 Solving Inequalities

Advertisements

Basic Algebra Grade: 9 th Gustavo Miranda LRC 320.

Solving Linear Equations

Solve Multi-step Equations (var. both sides) Students will solve multi-step equations with variables on both sides using distributive property, combining.

3-5 Solving Equations with the variable on each side Objective: Students will solve equations with the variable on each side and equations with grouping.

Solve an equation with variables on both sides

3-3 Solving Multiplication Equations. Solve Solution GOAL Find the value of the variable that makes the equation TRUE. The value that makes the equation.

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.

Standardized Test Practice

Algebraic Expressions

An equation is a mathematical statement that two expressions are equivalent. The solution set of an equation is the value or values of the variable that.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 2.3.

1. solve equations with variables on both sides. 2. solve equations containing grouping symbols. 3.5 Objectives The student will be able to:

Solve Equations with Variables on Both Sides

Linear Equations in One variable Nonlinear Equations 4x = 8 3x – = –9 2x – 5 = 0.1x +2 Notice that the variable in a linear equation is not under a radical.

EXAMPLE 1 Solve an equation with variables on both sides 7 – 8x = 4x – 17 7 – 8x + 8x = 4x – x 7 = 12x – = 12x Write original equation. Add.

1.4 Solving Equations ●A variable is a letter which represents an unknown number. Any letter can be used as a variable. ●An algebraic expression contains.

Entry Task ? LT: I can solve equations and problems by writing equations.

3-2 Solving Equations by Using Addition and Subtraction Objective: Students will be able to solve equations by using addition and subtraction.

Algebra II Honors POD Homework: p odds, odds (you must use completing the square), and 77, 83 Find all real solutions for the following:

Notes 2.4– Solving Equations with Variables on Both Sides.

§ 1.2 Graphing Linear Equations. Martin-Gay, Beginning and Intermediate Algebra, 4ed 22 Linear Equation in Two Variables A linear equation in two variables.

§ 2.3 The Multiplication Property of Equality. Martin-Gay, Beginning Algebra, 5ed 22 Multiplication Property of Equality If a, b, and c are real numbers,

Solving Equations. The equations are equivalent If they have the same solution(s)

2-1 Solving Linear Equations and Inequalities Warm Up

Let Me See You 1-2 Step Two-Step Algebraic Equations.

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.

Section 4.3 Solving Absolute Value Equations and Inequalities

§ 2.2 The Addition Property of Equality. Angel, Elementary Algebra, 7ed 2 Linear Equations A linear equation in one variable is an equation that can be.

Trigonometric Equations 5.5. To solve an equation containing a single trigonometric function: Isolate the function on one side of the equation. Solve.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 8.1.

1.4 Solving Multi-Step Equations. To isolate the variable, perform the inverse or opposite of every operation in the equation on both sides of the equation.

Steps for Solving Equations with Variables on Both Sides 1.Distribute when necessary. 2.Combine like terms if possible. 3.Add or subtract to get the variables.

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.

6-2 Solving Systems Using Substitution Hubarth Algebra.

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.

1) Solve. -5t = 60 To get the variable by itself, which number needs to be moved? -5 To move the -5, you have to do the opposite operation. What operation.

Section 2.5 – Quadratic Equations

6-3: Solving Equations with variables on both sides of the equal sign

Equations Quadratic in form factorable equations

Example: Solve the equation. Multiply both sides by 5. Simplify both sides. Add –3y to both sides. Simplify both sides. Add –30 to both sides. Simplify.

Copyright 2013, 2009, 2005, 2002 Pearson, Education, Inc.

CHAPTER 1.3 Solving Equations.

Students will solve two step equations (12-4).

Math , 2.2, 2.3 Linear Equations.

Solve for variable 3x = 6 7x = -21

2 Understanding Variables and Solving Equations.

Math Objective: Solve Two-Step Equations

Warm – Up #11 .

6-2 Solving Systems Using Substitution

Algebraic Equations Solving One Step Equations with Whole Numbers

Equations with Unknowns on Both Sides

3-4A Solving Multi-Step Inequalities

3-4B Solving Inequalities with Special Solutions

SECTION 9-3 : SOLVING QUADRATIC EQUATIONS

Solving Systems using Substitution

Solving Equations with variables on each side

1.3 Solving Linear Equations

2.1 Solving Linear Inequalities

- Finish Unit 1 test - Solving Equations variables on both sides

2.1 – 2.2 Solving Linear Inequalities

SECTION 2-4 : SOLVING EQUATIONS WITH THE VARIABLE ON BOTH SIDES

Section Solving Linear Systems Algebraically

Algebra 1 Section 2.7.

2-3 Equations With Variables on Both Sides

Warm-Up Set 1: Factor. 1) x2 + 6x + 9 2) x2 - 10x + 25 Set 2: Factor.

3-6 Absolute Value Equations and Inequalities

Solving Equations With One Variable

1.3 Solving Linear Equations

Bellwork Graph on a number line 1.) x < 4 2.) y ≥ -2 3.) x ≤ 0

Presentation transcript:

Ch. 2 Vocabulary ( continued) 8.) identity 9.) literal equation 10.) formula

2-4 Solving Equations with Variables on Both Sides Algebra 1

Add an extra Step to Solving Eq.’s After you SIMPLIFY, then you should ADD THE OPPOSITE of either variable to both sides. Then you can ADD THE OPPOSITE of the constants or numbers without variables, etc…

Example 1 Solve: 5x – 6 = 3x + 9

Example 1 (Cont’d) Solve: 5x – 6 = 3x + 9 -3x -3x Add the Opp. Of Var.

Example 1 (Cont’d) Solve: 5x – 6 = 3x + 9 -3x -3x Add the Opp. Of Var.

Example 1 (Cont’d) Solve: 5x – 6 = 3x + 9 -3x -3x Add the Opp. Of Var. +6 +6 Add the Opp. Of No.’s

Example 1 (Cont’d) Solve: 5x – 6 = 3x + 9 -3x -3x Add the Opp. Of Var. +6 +6 Add the Opp. Of No.’s 2x = 15

Example 1 (Cont’d) Solve: 5x – 6 = 3x + 9 -3x -3x Add the Opp. Of Var. +6 +6 Add the Opp. Of No.’s 2x = 15 2 2 Divide by the coeff.

Example 1 (Cont’d) 5x – 6 = 3x + 9 -3x -3x Add the Opp. Of Var. +6 +6 Add the Opp. Of No.’s 2x = 15 2 2 Divide by the coeff. x = 7 ½ Solution

Example 2 Solve: 5m + 4 = 7(m + 1) – 2m

Example 2(Cont’d) Solve: 5m + 4 = 7(m + 1) – 2m 5m + 4 = 7m + 7 – 2m Simplify-Dist.Prop.

Example 2 (Cont’d) Solve: 5m + 4 = 7(m + 1) – 2m 5m + 4 = 7m + 7 – 2m Simplify-Dist.Prop. 5m + 4 = 5m + 7 Simplify-Add Like Terms

Example 2 (Cont’d) Solve: 5m + 4 = 7(m + 1) – 2m 5m + 4 = 7m + 7 – 2m Simplify-Dist.Prop. 5m + 4 = 5m + 7 Simplify-Add Like -5m -5m (Add the Opp.) Terms

Example 2 ( Cont’d) Solve: 5m + 4 = 7(m + 1) – 2m 5m + 4 = 7m + 7 – 2m Simplify-Dist.Prop. 5m + 4 = 5m + 7 Simplify-Add Like -5m -5m (Add the Opp.) Terms 4 7 4 does not equal 7, so there is NO Solution

Example 2 ( Cont’d) No Solution can be written as a symbol, an O with a slash through it, .

Ex. 3) 7(4 - y) = 3(y - 4)

Ex. 4 2y + 4 = 2(y + 2)

All Real Numbers as a Solution If you have an answer where the left side does equal the right side (4=4), then the solution involves all Real Numbers. Usually, we represent Real Numbers as a capitalized cursive R, like .

Three Possible Solutions Let’s review the three possible solutions! x = ? No Solution or when a number does not equal another number (4 7). All Real Numbers or when a number equals itself ( 4 = 4).