Beginning Algebra, 11th Edition

7.8 Variation

Solving Variation Problems

Step 1 Write the variation equation.

or Direct variation

or Inverse variation

Step 2 Find kby substituting the appropriate given
values of xand yinto the equation.

Step 3 Rewrite the variation equation with the value of
kfrom Step 2.

Step 4 Substitute the remaining values, and solve for
the unknown.

y

k

xn

y

k

x

ykx ykxn

If yvaries inversely as x, and when find ywhen

The equation for inverse variation is as follows.

Substitute given values.

Multiply by 9. Rewrite.

y= Let x=6.

36

6

= 6

y= k= 36

36

x

k= 36

4 =

k

9

y=

k

x

y= 4 x=9, x=6.

CONCEPTS EXAMPLES

REVIEW EXERCISES

CHAPTER 7

7.1 Find the numerical value of each rational expression for (a) and (b).

Find any values of the variable for which each rational expression is undefined. Write answers

with the symbol.

6.How do you determine the values of the variable for which a rational expression is

undefined?

Write each rational expression in lowest terms.

Write four equivalent forms for each rational expression.

11. 12.-

8 - 3 x

3 - 6 x

4 x- 9

2 x+ 3

4 p^2 + 8 pq- 5 q^2

10 p^2 - 3 pq-q^2

4 x^2 - 9

6 - 4 x

m- 4

4 - m

5 a^3 b^3

15 a^4 b^2

2 k+ 1

3 k^2 + 17 k+ 10

y+ 3

2 y

4

x- 3

Z

3 x

x^2 - 4

4 x- 3

5 x+ 2

x=- 2 x= 4

CHAPTER 7 Review Exercises 487