3.1 Solving Two-Step Equations 1 3x + 7 = –5 3x + 7 = –5 – 7 – 7

Slides:

Advertisements

Similar presentations

3 3 . Solving Two-Step Equations Activity Modeling Two-Step Equations

Advertisements

Solving Two-Step Equations

Solve an equation with variables on both sides

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

Solve an equation using subtraction EXAMPLE 1 Solve x + 7 = 4. x + 7 = 4x + 7 = 4 Write original equation. x + 7 – 7 = 4 – 7 Use subtraction property of.

 Start Bellwork #37  Write out the questions!  HW, red pen, book, pencil on desk.

Standardized Test Practice

Solving a System of Equations by ELIMINATION. Elimination Solving systems by Elimination: 1.Line up like terms in standard form x + y = # (you may have.

Standardized Test Practice

Standardized Test Practice

© 2007 by S - Squared, Inc. All Rights Reserved.

Solving Two-Step Equations You will solve equations by undoing operations using properties of equality. Essential Question: How do you solve two-step equations?

Chapter 3 Lesson 5 Solving 2-Step Equations Pgs What you will learn: To solve 2-step equations!

3.1 Solving Equations Algebra I.

Lesson 1.1 Objective: To solve equations using addition, subtraction, multiplication, and division Are operations that undo each other such as addition.

One step equations Add Subtract Multiply Divide  When we solve an equation, our goal is to isolate our variable by using our inverse operations.  What.

Algebra 1 Solve 13 = + 5. y3y3 24 = y Simplify. 13 – 5 = + 5 – 5Subtract 5 from each side. y3y3 8 = Simplify. y3y3 3 8 = 3 Multiply each side by 3. y3y3.

Lesson 1-8 Solving Addition and Subtraction Equations.

Lesson 2 Contents Example 1Solve a Two-Step Equation Example 2Solve Two-Step Equations Example 3Solve Two-Step Equations Example 4Equations with Negative.

Solve an equation using addition EXAMPLE 2 Solve x – 12 = 3. Horizontal format Vertical format x– 12 = 3 Write original equation. x – 12 = 3 Add 12 to.

Example 1 Solving Two-Step Equations SOLUTION a. 12x2x + 5 = Write original equation. 112x2x + – = 15 – Subtract 1 from each side. (Subtraction property.

Solve an inequality using multiplication EXAMPLE 2 < 7< 7 x –6 Write original inequality. Multiply each side by –6. Reverse inequality symbol. x > –42.

EXAMPLE 1 Solve a two-step equation Solve + 5 = 11. x 2 Write original equation. + 5 = x – 5 = x 2 11 – 5 Subtract 5 from each side. = x 2 6 Simplify.

Use the substitution method

Example 2 Multiple Choice Practice

Splash Screen. Then/Now Solve equations by using addition and subtraction. Solve equations by using multiplication and division.

Solve one step equations. You can add the same amount to both sides of an equation and the statement will remain true = = 9 x = y +

Multiply one equation, then add

© 2007 by S - Squared, Inc. All Rights Reserved.

2.2 Solving Two- Step Equations. Solving Two Steps Equations 1. Use the Addition or Subtraction Property of Equality to get the term with a variable on.

Solve a two-step equation by combining like terms EXAMPLE 2 Solve 7x – 4x = 21 7x – 4x = 21 Write original equation. 3x = 21 Combine like terms. Divide.

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 +

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 So far you have followed these steps to solve equations with fractions: Undo any addition or subtraction in order to get the variable term alone on one.

Solving a System of Equations by ELIMINATION. Elimination Solving systems by Elimination: 1.Line up like terms in standard form x + y = # (you may have.

1.4 Solving Equations.

Solving Absolute-Value Equations

3. 3 Solving Equations Using Addition or Subtraction 3

EXAMPLE 2 Rationalize denominators of fractions Simplify

Solve One-Step Multiplication and Division Equations

Solving Two-Step Equations

3-1 HW:Pg #4-28eoe, 30-48e, 55, 61,

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

Solve an equation by multiplying by a reciprocal

3.1 Solving Two-Step Equations

2 Understanding Variables and Solving Equations.

Solving Systems by Elimination

Warm up 11/1/ X ÷ 40.

Solving 1-Step Integer Equations

Warm Up Simplify each expression. 1. 3x + 2y – 5x – 2y

Solving One-Step Equations

Solve an equation by combining like terms

Objective Solve one-step equations in one variable by using multiplication or division.

Objectives Solve systems of linear equations in two variables by elimination. Compare and choose an appropriate method for solving systems of linear equations.

Solving Multi-Step Equations

Solving one- and two-step equations

Main Idea and New Vocabulary Example 1: Solve Two-Step Equations

Objective Solve one-step equations in one variable by using multiplication or division.

Solving Absolute-Value Equations

Solving Absolute-Value Equations

Learning Objective Students will be able to: Solve equations in one variable that contain absolute-value expressions.

Lesson 1.1 Objective: To solve equations using addition, subtraction, multiplication, and division Vocab: Inverse operations: Are operations that undo.

Solving Systems by Elimination

Exercise In what order would you perform these operations? 2 + 3(4)

Skill Check Lesson Presentation Lesson Quiz.

Solving Equations.

Example 2B: Solving Linear Systems by Elimination

Solving Equations by 2-1 Adding or Subtracting Warm Up

Presentation transcript:

3.1 Solving Two-Step Equations 1 3x + 7 = –5 3x + 7 = –5 – 7 – 7 LESSON Solving Two-Step Equations EXAMPLE 1 Using Subtraction and Division to Solve Solve 3x + 7 = –5. Check your solution. SOLUTION 3x + 7 = –5 Write original equation. 3x + 7 = –5 – 7 – 7 Subtract 7 from each side. 3x = –12 Simplify. 3x = –12 3 3 = Divide each side by 3. x = –4 Simplify. ANSWER The solution is –4.

3.1 Solving Two-Step Equations 1 3x + 7 = –5 3(–4) + 7 = –5 –5 = –5 LESSON Solving Two-Step Equations EXAMPLE 1 Using Subtraction and Division to Solve Solve 3x + 7 = –5. Check your solution. ANSWER The solution is –4. CHECK 3x + 7 = –5 Write original equation. 3(–4) + 7 = –5 ? Substitute –4 for x. –5 = –5 Solution checks.

3.1 Solving Two-Step Equations 2 – 3 = 1 – 3 = 1 + 3 + 3 = 4 ( ) = (4) LESSON Solving Two-Step Equations EXAMPLE 2 Using Addition and Multiplication to Solve Solve – 3 = 1. Check your solution. x 2 SOLUTION – 3 = 1 x 2 Write original equation. – 3 = 1 x 2 + 3 + 3 Add 3 to each side. = 4 x 2 Simplify. ( ) = (4) x 2 2 2 Multiply each side by 2. x = 8 Simplify. ANSWER The solution is 8.

3.1 Solving Two-Step Equations 2 – 3 = 1 – 3 = 1 1 = 1 LESSON Solving Two-Step Equations EXAMPLE 2 Using Addition and Multiplication to Solve Solve – 3 = 1. Check your solution. x 2 ANSWER The solution is 8. CHECK – 3 = 1 x 2 Write original equation. – 3 = 1 8 2 ? Substitute 8 for x. 1 = 1 Solution checks.

3.1 Solving Two-Step Equations 3 7 – 4y = 19 7 – 4y = 19 – 7 – 7 LESSON Solving Two-Step Equations EXAMPLE 3 Solving an Equation with Negative Coefficients Solve 7 – 4y = 19. Check your solution. SOLUTION 7 – 4y = 19 Write original equation. 7 – 4y = 19 – 7 – 7 Subtract 7 from each side. –4y = 12 Simplify. –4y = 12 –4 –4 = Divide each side by –4. x = –3 Simplify. ANSWER The solution is –3.

3.1 Solving Two-Step Equations 3 7 – 4y = 19 7 – 4(–3) = 19 19 = 19 LESSON Solving Two-Step Equations EXAMPLE 3 Solving an Equation with Negative Coefficients Solve 7 – 4y = 19. Check your solution. ANSWER The solution is –3. CHECK 7 – 4y = 19 Write original equation. 7 – 4(–3) = 19 ? Substitute –3 for y. 19 = 19 Solution checks.

3.1 Solving Two-Step Equations LESSON Solving Two-Step Equations Drum Set You are buying a drum set that costs $495. The music store lets you make a down payment. You can pay the remaining cost in three equal monthly payments with no interest charged. You make a down payment of $150. How much is each monthly payment? You will see how to answer this question by writing and solving a two-step equation. You can solve a two-step equation by using two inverse operations.

3.1 Solving Two-Step Equations 4 495 = 150 + 3p LESSON Solving Two-Step Equations EXAMPLE 4 Writing and Solving a Two-Step Equation Find the monthly payment for the drum set described on Slide 1. SOLUTION Let p represent the monthly payment. Write a verbal model. Total cost of drum set = Amount of down payment + Monthly payment Number of months • 495 = 150 + 3p Substitute.

3.1 Solving Two-Step Equations 4 495 = 150 + 3p 495 = 150 + 3p LESSON Solving Two-Step Equations EXAMPLE 4 Writing and Solving a Two-Step Equation Find the monthly payment for the drum set described on Slide 1. SOLUTION Substitute. 495 = 150 + 3p 495 = 150 + 3p – 150 – 150 Subtract 150 from each side. 345 = 3p Simplify. 345 3p 3 3 = Divide each side by 3. 115 = p Simplify. ANSWER The monthly payment is $115.