Algebra 2 and Trigonometry

Ann Xavier Gantert

Chapter 2

THE RATIONAL NUMBERS - all with Video Answers

Educators

Section 7

Solving Rational Equations

Problem 1

Samantha said that the equation $\frac{a-2}{a}=\frac{a+2}{2 a}$ in Example 2 could be solved by multiplying both sides of the equation by 2$a$ . Would Samantha's solution be the same as the solution
obtained in Example 2$?$ Explain why or why not.

Derrick H.

Derrick H.

Numerade Educator

Problem 2

Brianna said that $\frac{3}{x-2}=\frac{5}{x+2}$ is a rational equation but $\frac{x-2}{3}=\frac{x+2}{5}$ is not. Do you agree with Brianna? Explain why or why not.

Dilip P.

Numerade Educator

Problem 3

In $3-20,$ solve each equation and check.
$$
\frac{1}{4} a+8=\frac{1}{2} a
$$

Derrick H.

Numerade Educator

Problem 4

In $3-20,$ solve each equation and check.
$$
\frac{3}{4} x=14-x
$$

Dilip P.

Numerade Educator

Problem 5

In $3-20,$ solve each equation and check.
$$
\frac{x+2}{5}=\frac{x-2}{3}
$$

Derrick H.

Numerade Educator

Problem 6

In $3-20,$ solve each equation and check.
$$
\frac{x}{5}-\frac{x}{10}=7
$$

Dilip P.

Numerade Educator

Problem 7

In $3-20,$ solve each equation and check.
$$
\frac{2 x}{3}+1=\frac{3 x}{4}
$$

Derrick H.

Numerade Educator

Problem 8

In $3-20,$ solve each equation and check.
$$
x-0.05 x=19
$$

Dilip P.

Numerade Educator

Problem 9

In $3-20,$ solve each equation and check.
$$
0.4 x+8=0.5 x
$$

Derrick H.

Numerade Educator

Problem 10

In $3-20,$ solve each equation and check.
$$
0.2 a=0.05 a+3
$$

Dilip P.

Numerade Educator

Problem 11

In $3-20,$ solve each equation and check.
$$
1.2 b-3=7-0.05 b
$$

Derrick H.

Numerade Educator

Problem 12

In $3-20,$ solve each equation and check.
$$
\frac{x}{x+5}=\frac{2}{3}
$$

Dilip P.

Numerade Educator

Problem 13

In $3-20,$ solve each equation and check.
$$
\frac{7}{2 x-3}=\frac{4}{x}
$$

Derrick H.

Numerade Educator

Problem 14

In $3-20,$ solve each equation and check.
$$
\frac{3}{a}+\frac{1}{2}=\frac{11}{5 a}
$$

Dilip P.

Numerade Educator

Problem 15

In $3-20,$ solve each equation and check.
$$
18-\frac{4}{b}=10
$$

Derrick H.

Numerade Educator

Problem 16

In $3-20,$ solve each equation and check.
$$
\frac{x}{2}=\frac{3}{2 x+1}
$$

Dilip P.

Numerade Educator

Problem 17

In $3-20,$ solve each equation and check.
$$
1=\frac{5}{x+3}+\frac{5}{(x+2)(x+3)}
$$

Derrick H.

Numerade Educator

Problem 18

In $3-20,$ solve each equation and check.
$$
\frac{a-1}{4}=\frac{8}{a+3}
$$

Dilip P.

Numerade Educator

Problem 19

In $3-20,$ solve each equation and check.
$$
\frac{4}{y+2}=1-\frac{8}{y(y+2)}
$$

Derrick H.

Numerade Educator

Problem 20

In $3-20,$ solve each equation and check.
$$
\frac{4}{3 b-2}-\frac{7}{3 b+2}=\frac{1}{9 b^{2}-4}
$$

Dilip P.

Numerade Educator

Problem 21

Last week, the ratio of the number of hours that Joseph worked to the number of hours that Nicole worked was $2 : 3 .$ This week Joseph worked 4 hours more than last week and Nicole worked twice as many hours as last week. This week the ratio of the hours Joseph worked to the number of hours Nicole worked is $1 : 2 .$ How many hours did each person work each week?

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Problem 22

Anthony rode his bicycle to his friend's house, a distance of 1 mile. Then his friend's mother drove them to school, a distance of 12 miles. His friend's mother drove at a rate that is 25 miles per hour faster than Anthony rides his bike. If it took Anthony $\frac{3}{5}$ of an hour to get to school, at what average rate does he ride his bicycle? (Use distance $=$ time for each part of the trip to school.)

Dilip P.

Numerade Educator

Problem 23

Amanda drove 40 miles. Then she increased her rate of speed by 10 miles per hour and drove another 40 miles to reach her destination. If the trip took 1$\frac{4}{5}$ hours, at what rate did Amanda drive?

Evelyn C.

Numerade Educator

Problem 24

Last week, Emily paid $\$ 8.25$ for $x$ pounds of apples. This week she paid $\$ 9.50$ for $(x+1)$ pounds of apples. The price per pound was the same each week. How many pounds of apples did Emily buy each week and what was the price per pound? (Use $\frac{\text { total cost }}{\text { number of pounds }}=$ cost per pound for each week.)

Dilip P.

Numerade Educator