Intermediate Algebra (11th edition)

2.4 Further Applications of Linear

Equations

To solve a uniform motion problem, draw a sketch and
make a table. Use the formula

drt.

Two cars start from towns 400 mi apart and travel toward each other.

They meet after 4 hr. Find the rate of each car if one travels 20 mph

faster than the other.

Let.

Then x+ 20 =rate of the faster car.

x=rate of the slower car in miles per hour

CONCEPTS EXAMPLES

(continued)

Use the information in

the problem and

to complete a table.

d=rt

A sketch shows that the sum of the distances, 4xand must

be 400.

The equation is

Solving this equation gives The slower car travels 40 mph,

and the faster car travels 40 + 20 = 60 mph.

x=40.

4 x+ 41 x+ 202 =400.

400

4 x 4(x + 20)

41 x+ 202 ,

CHAPTER 2 Summary 125

Rate Time Distance

Slower Car x 44 x

Faster Car 4

400 Total

x+ 20 41 x+ 202

2.5 Linear Inequalities in One Variable

Solving a Linear Inequality in One Variable

Step 1 Simplify each side of the inequality by clearing
parentheses and combining like terms.

Step 2 Use the addition property of inequality to get
all terms with variables on one side and all
terms without variables on the other side.

Step 3 Use the multiplication property of inequality to
write the inequality in one of these forms.

If an inequality is multiplied or divided by a negative
number, the inequality symbol must be reversed.

x 6 k, x...k, x 7 k, or xÚk

Solve

Distributive property

Subtract 6.

Divide by.

Change to

The solution set, , is graphed here.

–3 –2 –1 0 1 2 3

3 - 3, q 2

xÚ- 3

... Ú.

-^2 x -^2

• 2

Ú

6

- 2

• 2 x... 6


• 2 x+ 6 - 6 ... 12 - 6


• 2 x+ 6 ... 12

3 x+ 6 - 5 x... 12

31 x+ 22 - 5 x...12.

To solve a three-part inequality, work with all three parts
at the same time.

Solve

Subtract 3.

Divide by 2.

The solution set, is graphed here.

–4 –3 –2 –1 0 1 2

A-^72 , 2D,

-

7

2

6 x ... 2

- 7

2

6

2 x

2

...

4

2

• 76 2 x ... 4


• 4 - 36 2 x+ 3 - 3 ... 7 - 3


• 462 x+ 3 ...7.