Standardized Test Practice EXAMPLE 4 ANSWER The correct answer is B. DCBA Simplify the expression 4(n + 9) – 3(2 + n). 4(n + 9) – 3(2 + n) = Distributive.

Slides:

Advertisements

Similar presentations

Write an equation given the slope and a point

Advertisements

EXAMPLE 1 Standardized Test Practice SOLUTION Substitute several values of h into the equation C = h and solve for C.Then identify the table that.

Write an equation given the slope and a point EXAMPLE 2 Write an equation of the line that passes through (5, 4) and has a slope of –3. Because you know.

Warm-Up Exercises 1. Solve |x – 6| = Solve |x + 5| – 8 = 2. ANSWER 2, 10 ANSWER –15, 5 3. A frame will hold photographs that are 5 inches by 8 inches.

• Write an inequality that describes your goal in terms of x and y.

Objective: To graph linear inequalities in two variables.

EXAMPLE 3 Standardized Test Practice SOLUTION

Solve an equation with variables on both sides

EXAMPLE 5 Solve a multi-step problem LIBRARY

Solve an equation by combining like terms

EXAMPLE 6 Solve a multi-step problem Job Earnings You have two summer jobs at a youth center. You earn $8 per hour teaching basketball and $10 per hour.

EXAMPLE 3 Combining Like Terms a. 3x + 4x = (3 + 4)x = 7x b.

Standardized Test Practice

EXAMPLE 5 Solve a multi-step problem Recording Studio

EXAMPLE 5 Simplify a mathematical model Digital Photo Printing You send 15 digital images to a printing service that charges $. 80 per print in large format.

EXAMPLE 1 Collecting Like Terms x + 2 = 3x x + 2 –x = 3x – x 2 = 2x 1 = x Original equation Subtract x from each side. Divide both sides by x2x.

Standardized Test Practice

Standardized Test Practice

Algebra Distributive Property. Vocabulary Equivalent expressions: two expressions that have the same output value for every input value Distributive.

Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.

Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.

3-2 HW: Pg #4-34e, 38, 40, ) B 47.) C.

EXAMPLE 2 Rationalize denominators of fractions Simplify

2.5 Solving equations with variables on both sides

Read a problem and make a plan EXAMPLE 1 Running You run in a city where the short blocks on north-south streets are 0.1 mile long. The long blocks on.

EXAMPLE 3 Write the standard equation of a circle The point (–5, 6) is on a circle with center (–1, 3). Write the standard equation of the circle. SOLUTION.

Solve an equation by combining like terms EXAMPLE 1 8x – 3x – 10 = 20 Write original equation. 5x – 10 = 20 Combine like terms. 5x – =

The Distributive Property Objective Key Vocabulary equivalent expressions distributive property.

Multi Step Equations Copied from =ie7&rls=com.microsoft:en-us:IE- Address&ie=&oe=#hl=en&tbo=d&rls=com.microsoft:en-us:IE-

1 Fitness You work out each day after school by jogging around a track and swimming laps in a pool. You will see how to write and simplify a variable expression.

Multi-Step Equations We must simplify each expression on the equal sign to look like a one, two, three step equation.

2.4 Solve Multi-Step Equations

EXAMPLE 1 Solve by equating exponents Rewrite 4 and as powers with base Solve 4 = x 1 2 x – 3 (2 ) = (2 ) 2 x – 3x – 1– 1 2 = 2 2 x– x + 3 2x =

Warm Up Solve. 1. 3x = = z – 100 = w = 98.6 x = 34 y = 225 z = 121 w = 19.5 y 15.

Systems of Equations: Substitution

Use the substitution method

EXAMPLE 1 Apply the distributive property

EXAMPLE 4 Solve a system using substitution Marketing The marketing department of a company has a budget of $30,000 for advertising. A television ad costs.

Solve Linear Systems by Substitution Students will solve systems of linear equations by substitution. Students will do assigned homework. Students will.

Y=3x+1 y 5x + 2 =13 Solution: (, ) Solve: Do you have an equation already solved for y or x?

EXAMPLE 2 Multiply by the LCD Solve. Check your solution. x – 2 x = SOLUTION x – 2 x = Multiply by LCD, 5(x – 2). 5(x – 2) x – 2 x 1 5.

2.5 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply the Distributive Property.

EXAMPLE 4 Using a Verbal Model You pay $20 for a youth center membership. Drum lessons at the center cost $8 each for members and $12 each for nonmembers.

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.

Example 1 Read a problem and make a plan

Solving Multi-Step Equations One Step at a Time !!!!!

1.–15 + (–19) + 16 = ANSWER –18 2.6(–x)(–4) = ANSWER 24x Warm-Up for Lesson 2.6 ? ?

Lesson 2.3 Simplifying Variable Expressions Essential Question: How do you simplify variable expressions?

Objective: Students will solve multistep equations using the property of opposites and combining like terms Standard: 4.0 Students simplify expressions.

2.3 Simplifying Variable Expressions

Solve the equation. 1. 6a – 3 + 2a = 13 ANSWER a = 2

Solving Multistep Equations

EXAMPLE 2 Rationalize denominators of fractions Simplify

Skill Check Lesson Presentation Lesson Quiz.

EXAMPLE 5 Simplify a mathematical model Digital Photo Printing

Apply the Distributive Property

Chapter 2 Review 14 questions: 1 – write a verbal expression

Solve an equation by multiplying by a reciprocal

Writing Equations of a Line

Solving Systems using Substitution

Solve a system of linear equation in two variables

Solving Systems of Equations using Substitution

Lesson 2.5 Apply the Distributive Property

Solve an equation by combining like terms

Solving Multi-Step Equations

} 2x + 2(x + 2) = 36 2x + 2x + 4 = 36 4x + 4 = x =

Evaluating expressions and Properties of operations

2.3 Simplifying Variable Expressions

MS Algebra A-SSE-1b – Ch. 2.5 Expressions with Distributive Property

Simplify by combining like terms

Presentation transcript:

Standardized Test Practice EXAMPLE 4 ANSWER The correct answer is B. DCBA Simplify the expression 4(n + 9) – 3(2 + n). 4(n + 9) – 3(2 + n) = Distributive property = n + 30 Combine like terms. A B C D n + 3 5n + 30 n + 305n + 3 4n + 36 – 6 – 3n

Solve a multi-step problem EXAMPLE 5 EXERCISING Your daily workout plan involves a total of 50 minutes of running and swimming. You burn 15 calories per minute when running and 9 calories per minute when swimming. Let r be the number of minutes that you run. Find the number of calories you burn if you run for 20 minutes. SOLUTION The workout lasts 50 minutes, and your running time is r minutes. So, your swimming time is (50 – r) minutes.

Solve a multi-step problem EXAMPLE 5 STEP 1 C = Write equation. = 15 r – 9r Distributive property = 6r Combine like terms. Write a verbal model. Then write an equation. 15r + 9(50 – r) C = 5 r + 9 (50 – r) Amount burned (calories) Burning rate when running (calories/minute) Running time (minutes) Swimming time (minutes) = + Burning rate when swimming (calories/minute)

Solve a multi-step problem EXAMPLE 5 C = Write equation. = 6(20) = 570 Substitute 20 for r. Then simplify. ANSWER You burn 570 calories in your 50 minute workout if you run for 20 minutes and swim for 30 minutes. STEP 2 Find the value of C when r = 20. 6r + 450

GUIDED PRACTICE for Examples 4 and 5 6. Simplify the expression 5(6 + n) – 2(n – 2) = n. 7. WHAT IF ? In Example 5, suppose your workout lasts 45 minutes. How many calories do you burn if you run for 20 minutes ? 30 minutes ? ANSWER You burn 525 calories in your 45 minute workout if you run for 20 minutes. You burn 585 calories in your 45 minute workout if you run for 30 minutes.