Teacher – Mrs. Volynskaya Algebra 2 Absolute Value Equations Absolute value A numbers distance from 0 on number line. ALWAYS POSITIVE!!! Extraneous Solution.

Slides:

Advertisements

Similar presentations

Solving Rational Equations and Inequalities

Advertisements

Warm-Up  |x |=3  |x |= -7  |2x |=10  |x+3 |=6.

2.2 Solve Absolute Value Equations and Inequalities

Prerequisite Skills VOCABULARY CHECK 1.

EXAMPLE 1 Solve a simple absolute value equation Solve |x – 5| = 7. Graph the solution. SOLUTION | x – 5 | = 7 x – 5 = – 7 or x – 5 = 7 x = 5 – 7 or x.

Solving Inequalities Objective: The student will be able to solve inequalities. Algebra 2.

Solve an absolute value equation EXAMPLE 2 SOLUTION Rewrite the absolute value equation as two equations. Then solve each equation separately. x – 3 =

EXAMPLE 1 Solve absolute value inequalities

1.8 Solving Absolute Value Equations and Inequalities

Absolute Value Inequality

How do I solve absolute value equations and inequalities?

Linear Equations, Inequalities, and Absolute Value

Set Operations and Compound Inequalities. 1. Use A = {2, 3, 4, 5, 6}, B = {1, 3, 5, 7, 9}, and C = {2, 4, 6, 8} to find each set.

Algebra II w/ trig. Compound inequality: two inequalities joined by “and” or “or” AND graph means both inequalities are true (think: between, alike) OR.

x x x < 1or x < 3 x < 3.

Solving Absolute Value Equations and Inequalities.

Expressions, Equations and Inequalities Ch. 1.6 Absolute Value Equations and Inequalities EQ: How can you solve absolute value equations and inequalities?

Solving Absolute Value Inequalities

Linear Inequalities And Absolute Value Solving Inequalities Multiplication/Division “ALGEBRA SWAG” “ALGEBRA SWAG” -

Lesson 5 Contents Glencoe McGraw-Hill Mathematics Algebra 2005 Example 1Solve an Absolute Value Equation Example 2Write an Absolute Value Equation.

3.6 Solving Absolute Value Equations and Inequalities

Factoring to Solve Quadratic Equations

1.6 Absolute Value Equations and Inequalities. Solving an Absolute Value Equation What is the solution of | 2x – 1 | = 5? Graph the solution. | 2x – 1.

Solving Open Sentences Involving Absolute Value

1.6 Absolute Value Inequalities and Equations Honors Algebra II.

1.7 – Solve Absolute Value Equations and Inequalities Recall that the absolute value of a number x, written |x|, is the distance the number is from 0 on.

Math 9 Lesson #23 – Absolute Value Equations and Inequalities Mrs. Goodman.

3.7 Absolute value DAY 2. Solve for x----no notes on this slide (just watch). |x| = 5 |x + 2| = 5 x = 5 or x = -5 x + 2 = 5 or x + 2 = -5 x =

Section 1-5: Absolute Value Equations and Inequalities Goal 2.08: Use equations and inequalities with absolute value to model and solve problems; justify.

1.7 “Absolute Value” Absolute Value is always positive!! 7 = 7-7 = 7 **When solving equations or inequalities, you MUST set up 2 separate problems, one.

Holt McDougal Algebra 2 Solving Rational Equations and Inequalities Solving Rational Equations and Inequalities Holt Algebra 2Holt McDougal Algebra 2.

1.8 Solving Absolute Value Equations and Inequalities Objectives: Write, solve, and graph absolute value equations and inequalities in mathematical and.

4.4 Absolute Value 11/14/12. Absolute Value: The distance of a number from 0 on a number line. Written as l x l Ex. |5| (distance of 5 from 0) = 5 Ex.

Algebra 2 Lesson 1-5 (Page 33) ALGEBRA 2 LESSON 1-5 Absolute Value Equations and Inequalities 1-1.

Section 2.7 Absolute Value Equations and Inequalities.

Absolute Value Graphs and Equations. Steps to find the equation of absolute value Find the vertex Change the ‘x’ value Put into equation y = |x | x value.

Warm Up  Solve the equation or inequality.  1.) 3x + 15 = -42  2.) 5x – 8 ≤ 7  3.) 2x

x + 5 = 105x = 10  x = (  x ) 2 = ( 5 ) 2 x = 5 x = 2 x = 25 (5) + 5 = 105(2) = 10  25 = 5 10 = = 10 5 = 5.

Solving Absolute Value Equations Absolute value is denoted by the bars |3|. Absolute value represents the distance a number is from 0. Thus, it is always.

EXAMPLE 1 Solve a system graphically Graph the linear system and estimate the solution. Then check the solution algebraically. 4x + y = 8 2x – 3y = 18.

Warm – up #6 Warm – up #6 Solutions x x x < 1or x < 3 x < 3.

1.8 Solving Absolute Value Equations and Inequalities Objectives: Write, solve, and graph absolute value equations and inequalities in mathematical and.

Algebra Solving Absolute Value Equations and Inequalities.

Jeopardy Q $100 Q $100 Q $100 Q $100 Q $100 Q $200 Q $200 Q $200

Notes Over 9.4 Checking a Solution Using a Graph The solution, or roots of an equation are the x-intercepts. Solve the equation algebraically. Check the.

Note #6 Standard: Solving Absolute-Value Equation and Inequalities Objective - To solve an equation involving absolute value.

Chapter 1.7 Solve Absolute Value Equations and Inequalities Analyze Situations using algebraic symbols; Use models to understand relationships.

Absolute Value Equations

Algebra 1 Section 6.4 Solve absolute Value Equations and Inequalities

Algebra 1 Section 6.5 Graph linear inequalities in two variables.

1. Add: 5 x2 – 1 + 2x x2 + 5x – 6 ANSWERS 2x2 +7x + 30

3.3 – Solving Systems of Inequalities by Graphing

10.8 Systems of Second-Degree Equations and Inequalities

To solve absolute value equations and inequalities in one variable

2.4 & 2.5 Absolute Value Inequalities and Equations

Algebra II 1.7: Solve Absolute Value Equations and Inequalities.

Ch 6.5 Absolute Value Equations

Solving Equations by Factoring and Problem Solving

Absolute Value inequalities

1.7: Solve Absolute Value Equations

SECTION 10-4 : RADICAL EQUATIONS

6.5 Solving Absolute Value Equations and Inequalities

Solving a Radical Equation

Absolute Value in Open Sentences

Jeopardy Final Jeopardy Solving Equations Solving Inequalities

Example 5A: Solving Simple Rational Equations

3-6 Absolute Value Equations and Inequalities

L1-5 Algebra 2.

Example 1: Solving Rational Equations

11-5 Solving Rational Equations

Presentation transcript:

Teacher – Mrs. Volynskaya Algebra 2 Absolute Value Equations Absolute value A numbers distance from 0 on number line. ALWAYS POSITIVE!!! Extraneous Solution A solution that appears to be a solution, but doesn’t work in the original equation.

1.5 Interpreting Absolute Value Equations Equation|x| = |x  0| = k MeaningThe distance between x and 0 is __k__. Graph Solutionsx  0 =  k or x  0 = k x = _  k_ or x = _k_

1.5 Interpreting Absolute Value Equations Equation|x  b| = k MeaningThe distance between x and b is _k_. Graph Solutionsx  b =  k or x  b = k x = _b  k_ or x = _b + k_

Teacher – Mrs. Volynskaya Algebra Solving an absolute value equation Use these steps to solve an absolute value equation | ax + b | = c where c > 0. Step 1 Write two equations: ax + b = _c_ or ax + b = _  c__. Step 2 Solve each equation. Step 3 Check each solution in the original _absolute value_ equation.

Example 1 Solve a simple absolute value equation Solve |x  3 | = 6. Graph the solution. x  3 = -6 or x  3 = x = -3 x = 9 These are the values that are 6 from 3 on the number line.

Example 2 Solve an absolute value equation Solve |4x + 10 | = 6x. Check for extraneous solutions. 4x + 10 = 6x or4x + 10 = -6x -4x -4x -4x-4x 10 = 2x10 = -10x 10/2 = 2x/2 10/-10 = -10x/-10 5 = x-1 = x CHECK

Example 2 Solve an absolute value equation Check |4x + 10 | = 6x | 4(_5_) + 10| ≟ 6(_5_) |4(  1_ ) + 10 | ≟ 6(_  1_) |_30_| ≟ _30_|_6_| ≟ _  6_ _30_ = _30__6_  _  6_ X = 5 x = -1 is rejected, because it is an extraneous solution.

1.5 Absolute Value Inequalities InequalityEquivalent Form |ax + b| _<_ c  c < ax + b < c Graph of Solution InequalityEquivalent Form |ax + b| _>_ c ax + b c Graph of Solution

Example 3 Solve an inequality Solve |2x + 5 | > 3. Then graph the solution. 2x x -2 2x/2 -2/2 x -1

Example 4 Solve an inequality Solve |x  1.5|  4.5. Then graph the solution. x – 1.5 ≤ 4.5 or x – 1.5 ≥ x ≤ 6 x ≥ -3