Alg 2 Lesson 1.3August 12, 2016

DO NOW (ON LOOSE LEAF)

EVEN PROBLEMS ONLY

KEY CONCEPTS AND VOCABULARY

Literal Equation - an equation that uses at least 2 letters as variables. You can solve for any variable “in terms of” the other variables.

EXAMPLE 2: SOLVING A LITERAL EQUATION

Solve each formula for the indicated variable.

a) b)

c) d)

3

4( y - 2) = x; for y

y - 7

x= x2; for y

y - 2 =

4

3x

y =

4

3x + 2

y - 7 = x3

y = x3 + 7

ax + bx - 3= -4, for x

ax + bx = -1

x(a + b) = -1

x =

-1

a + b

3V = pr 2h

h =

3V

pr 2

V =

1

3pr 2h, for h

Solve each equation for the indicated variable:

1. ax + bx – 15 = 0, for x 2. d = 2𝑥

𝑎+ b, for x

3. A = 1

2h(b1 + b2) , for h

INDEPENDENT PRACTICE

KEY CONCEPTS AND VOCABULARY

STEPS FOR SOLVING PROBLEMS:

1. Read the entire problem and identify important information

2. Set up an equation

3. Solve

4. Check the answer

EXAMPLE 3:WRITING AND SOLVING EQUATIONS IN REAL WORLD SITUATIONS

a) The first part of a play is 35 minutes longer than the second part. If the entire play is 155 minutes long, how long is the first part of the play? Write an equation to solve the problem.

x + (x - 35) =155

Part 1+ Part 2 =155

2x -35 =155

2x =190

x = 95

The first part of the

play is 95 minutes

b) A desktop computer now sells for 15% less than it did last year. The current price is $425. What was the price of the computer last year?

x - .15x = 425

.85x = 425

x = 500

The price of the computer

last year was $500

EXAMPLE 3:WRITING AND SOLVING EQUATIONS IN REAL WORLD SITUATIONS

c) Two buses leave Houston at the same time and travel in opposite directions. One bus averages 55 mi/h and the other bus averages 45 mi/h. When will they be 400 mi apart?

55t + 45t = 400

100t = 400

t = 4 4 hours

EXAMPLE 3:WRITING AND SOLVING EQUATIONS IN REAL WORLD SITUATIONS

d) The length of a rectangle is 3cm greater than its width. The perimeter is 24cm. What are the dimensions of the rectangle?

l = w+ 3

P = 2l + 2w = 24 l = 4.5+ 3

The dimensions of the rectangle

are 7.5cm by 4.5cm.

24 = 2(w+ 3)+ 2w

24 = 2w+6+ 2w

24 = 4w+6

18 = 4w

4.5 = w

l = 7.5

EXAMPLE 3:WRITING AND SOLVING EQUATIONS IN REAL WORLD SITUATIONS

e) Find four consecutive odd integers with a sum of 232.

x + (x + 2) + (x + 4) + (x + 6) = 232

4x +12 = 232

4x = 220

x = 55

55,57,59,61

EXAMPLE 3:WRITING AND SOLVING EQUATIONS IN REAL WORLD SITUATIONS

Write an equation and solve each problem:

1. Michael drove to a friend’s house at a rate of 40 mi/h. He returned by the same route at a rate of 45 mi/h. The driving time for the round trip was 4h. What is the distance Michael traveled?

2. The sides of a rectangle are in the ratio 3:2. What is the length of each side if the perimeter of a rectangle is 55 cm?

3. Find 4 consecutive odd integers with a sum of 184.

INDEPENDENT PRACTICE

RATE YOUR UNDERSTANDINGSOLVING EQUATIONS

MACC.912.A-CED.A.1: Create equations and inequalities in one variable and use them to solve

problems

RATING LEARNING SCALE

4 I am able to

• solve real world problems by writing equations

3

I am able to

• solve equations

• solve problems by writing equations

2

I am able to

• solve equations with help

• solve problems by writing equations with help

1

I am able to

• understand that you can use properties of equality and

inverse operations to solve equations

TARGET