ANSWER

1. 780 = 12.5r2. 9x + 25 = 178 ANSWER

62.417

ANSWER 113. 636 = 40g + 28(18 – g)

4. A balloon is released from a height of 5 feet above the ground. Its altitude (in feet) after t minutes is given by the expression 5 + 82t. What is the altitude of the balloon after 6 minutes?

ANSWER 497 ft

EXAMPLE 1 Use a formula

High-speed Train

The Acela train travels between Boston and Washington, a distance of 457 miles. The trip takes 6.5 hours. What is the average speed?

SOLUTION

You can use the formula for distance traveled as a verbal model.

457 = r 6.5

Distance (miles)

= Rate (miles/hour)

Time (hours)

-I

-C

EXAMPLE 1 Use a formula

An equation for this situation is 457 = 6.5r. Solve for r.

457 = 6.5r

70.3 r

Write equation.

Divide each side by 6.5.

The average speed of the train is about 70.3 miles per hour.

ANSWER

You can use unit analysis to check your answer.

457 miles 6.5 hours70.3 miles1 hour

CHECK

-A

-N

GUIDED PRACTICE for Example 1

1. AVIATION: A jet flies at an average speed of 540 miles per hour. How long will it take to fly from New York to Tokyo, a distance of 6760 miles?

Jet takes about 12.5 hours to fly from New York to Tokyo.

ANSWER

EXAMPLE 2 Look for a pattern

Paramotoring

A paramotor is a parachute propelled by a fan-like motor. The table shows the height h of a paramotorist t minutes after beginning a descent. Find the height of the paramotorist after 7 minutes.

I

EXAMPLE 2 Look for a pattern

SOLUTION

The height decreases by 250 feet per minute.

You can use this pattern to write a verbal model for the height.

An equation for the height is h = 2000 – 250t.

C

A

EXAMPLE 2 Look for a pattern

So, the height after 7 minutes is h = 2000 – 250(7) = 250 feet.

ANSWER N

EXAMPLE 3 Draw a diagram

BannersYou are hanging four championship banners on a wall in your school’s gym. The banners are 8 feet wide. The wall is 62 feet long. There should be an equal amount of space between the ends of the wall and the banners, and between each pair of banners. How far apart should the banners be placed?

SOLUTION

Begin by drawing and labeling a diagram, as shown below.

-I

-C

EXAMPLE 3 Draw a diagram

From the diagram, you can write and solve an equation to find x.

x + 8 + x + 8 + x + 8 + x + 8 + x = 62

5x + 32 = 62

Subtract 32 from each side.5x = 30

x = 6 Divide each side by 5.

Combine like terms.

Write equation.

The banners should be placed 6 feet apart.

ANSWER

-A

-N

EXAMPLE 4 Standardized Test Practice

SOLUTION

STEP 1 Write a verbal model. Then write an equation.

An equation for the situation is 460 = 30g + 25(16 – g).

EXAMPLE 4 Standardized Test Practice

Solve for g to find the number of gallons used on the highway.

STEP 2

460 = 30g + 25(16 – g)

460 = 30g + 400 – 25g

460 = 5g + 400

60 = 5g

12 = g

Write equation.

Distributive property

Combine like terms.

Subtract 400 from each side.

Divide each side by 5.

The car used 12 gallons on the highway.

ANSWER The correct answer is B.

CHECK: 30 12 + 25(16 – 12) = 360 + 100 = 460

GUIDED PRACTICE for Examples 2, 3 and 4

2. PARAMOTORING: The table shows the height h of a paramotorist after t minutes. Find the height of the paramotorist after 8 minutes.

So, the height after 8 minutes is h = 2400 – 210(8) = 720 ft

ANSWER

GUIDED PRACTICE for Examples 2, 3 and 4

3. WHAT IF? In Example 3, how would your answer change if there were only three championship banners?

The space between the banner and walls and between each pair of banners would increase to 9.5 feet.

ANSWER

GUIDED PRACTICE for Examples 2, 3 and 4

4. FUEL EFFICIENCY A truck used 28 gallons of gasoline and traveled a total distance of 428 miles. The truck’s fuel efficiency is 16 miles per gallon on the highway and 12 miles per gallon in the city. How many gallons of gasoline were used in the city?

Five gallons of gas were used.

ANSWER

EXAMPLE 1 Graph simple inequalities

a. Graph x < 2.

The solutions are all real numbers less than 2.

An open dot is used in the graph to indicate 2 is not a solution.

EXAMPLE 1 Graph simple inequalities

b. Graph x ≥ –1.

The solutions are all real numbers greater than or equal to –1.

A solid dot is used in the graph to indicate –1 is a solution.

EXAMPLE 2 Graph compound inequalities

a. Graph –1 < x < 2.

The solutions are all real numbers that are greater than –1 and less than 2.

EXAMPLE 2 Graph compound inequalities

b. Graph x ≤ –2 or x > 1.

The solutions are all real numbers that are less than or equal to –2 or greater than 1.

EXAMPLE 5 Solve an “and” compound inequality

Solve – 4 < 6x – 10 ≤ 14. Then graph the solution.

– 4 < 6x – 10 ≤ 14

– 4 + 10 < 6x – 10 + 10 ≤ 14 + 10

6 < 6x ≤ 24

1 < x ≤ 4

Write original inequality.

Add 10 to each expression.

Simplify.

Divide each expression by 6.

ANSWER

The solutions are all real numbers greater than 1 and less than or equal to 4. The graph is shown below.

EXAMPLE 6 Solve an “or” compound inequality

Solve 3x + 5 ≤ 11 or 5x – 7 ≥ 23. Then graph the solution.

SOLUTION

A solution of this compound inequality is a solution of either of its parts.

First Inequality Second Inequality

3x + 5 ≤ 11

3x ≤ 6

x ≤ 2

Write first inequality.

Subtract 5 from each side.

Divide each side by 3.

5x – 7 ≥ 23

5x ≥ 30

x ≥ 6

Write second inequality.

Add 7 to each side.

Divide each side by 5.

EXAMPLE 6 Solve an “or” compound inequality

ANSWER

The graph is shown below. The solutions are all real numbers less than or equal to 2 or greater than or equal to 6.

EXAMPLE 7 Write and use a compound inequality

Biology

A monitor lizard has a temperature that ranges from 18°C to 34°C. Write the range of temperatures as a compound inequality. Then write an inequality giving the temperature range in degrees Fahrenheit.

EXAMPLE 7 Write and use a compound inequality

SOLUTION

The range of temperatures C can be represented by the inequality 18 ≤ C ≤ 34. Let F represent the temperature in degrees Fahrenheit.

18 ≤ C ≤ 34 Write inequality.

18 ≤ ≤ 3459

(F – 32)

32.4 ≤ F – 32 ≤ 61.2

64.4 ≤ F ≤ 93.2

Substitute for C.95

(F – 32)

Multiply each expression by ,

the reciprocal of .

955

9Add 32 to each expression.

CLASSWORK

Workbook 1-5 (1-15 odd)Workbook 1-6 (1-23 odd)