<< Chapter < Page Chapter >> Page >

A man has 72 ft. of fencing to put around a rectangular garden. If the length is 3 times the width, find the dimensions of his garden.

Got questions? Get instant answers now!

A truck rental is $25 plus $.30/mi. Find out how many miles Ken traveled if his bill was $50.20.

84 mi

Got questions? Get instant answers now!

Complex Numbers

For the following exercises, use the quadratic equation to solve.

2 x 2 + 3 x + 7 = 0

x = 3 4 ± i 47 4

Got questions? Get instant answers now!

For the following exercises, name the horizontal component and the vertical component.

−2 i

horizontal component −2 ; vertical component −1

Got questions? Get instant answers now!

For the following exercises, perform the operations indicated.

( 9 i ) ( 4 7 i )

Got questions? Get instant answers now!

( 2 + 3 i ) ( 5 8 i )

7 + 11 i

Got questions? Get instant answers now!

( 3 5 i ) 2

−16 30 i

Got questions? Get instant answers now!

2 ( 8 5 )

−4 i 10

Got questions? Get instant answers now!

Quadratic Equations

For the following exercises, solve the quadratic equation by factoring.

3 x 2 + 18 x + 15 = 0

x = −1 , −5

Got questions? Get instant answers now!

  7 x 2 9 x = 0

x = 0 , 9 7

Got questions? Get instant answers now!

For the following exercises, solve the quadratic equation by using the square-root property.

( x 4 ) 2 = 36

x = 10 , −2

Got questions? Get instant answers now!

For the following exercises, solve the quadratic equation by completing the square.

4 x 2 + 2 x 1 = 0

x = 1 ± 5 4

Got questions? Get instant answers now!

For the following exercises, solve the quadratic equation by using the quadratic formula. If the solutions are not real, state No real solution .

15 x 2 x 2 = 0

x = 2 5 , 1 3

Got questions? Get instant answers now!

For the following exercises, solve the quadratic equation by the method of your choice.

x 2 = 10 x + 3

x = 5 ± 2 7

Got questions? Get instant answers now!

Other Types of Equations

For the following exercises, solve the equations.

x 1 2 4 x 1 4 = 0

x = 0 , 256

Got questions? Get instant answers now!

4 x 3 + 8 x 2 9 x 18 = 0

Got questions? Get instant answers now!

3 x 5 6 x 3 = 0

x = 0 , ± 2

Got questions? Get instant answers now!

3 x + 7 + x + 2 = 1

x = −2

Got questions? Get instant answers now!

| 2 x + 3 | 5 = 9

x = 11 2 , −17 2

Got questions? Get instant answers now!

Linear Inequalities and Absolute Value Inequalities

For the following exercises, solve the inequality. Write your final answer in interval notation.

2 x + 5 > x 7

( , 4 )

Got questions? Get instant answers now!

x 1 3 + x + 2 5 3 5

Got questions? Get instant answers now!

| 3 x + 2 | + 1 9

[ 10 3 , 2 ]

Got questions? Get instant answers now!

| x 3 | < −4

No solution

Got questions? Get instant answers now!

For the following exercises, solve the compound inequality. Write your answer in interval notation.

3 y < 1 2 y < 5 + y

( 4 3 , 1 5 )

Got questions? Get instant answers now!

For the following exercises, graph as described.

Graph the absolute value function and graph the constant function. Observe the points of intersection and shade the x -axis representing the solution set to the inequality. Show your graph and write your final answer in interval notation.

| x + 3 | 5

Got questions? Get instant answers now!

Graph both straight lines (left-hand side being y1 and right-hand side being y2) on the same axes. Find the point of intersection and solve the inequality by observing where it is true comparing the y -values of the lines. See the interval where the inequality is true.

x + 3 < 3 x 4

Where the blue is below the orange line; point of intersection is x = 3.5.

( 3.5 , )


A coordinate plane with the x and y axes ranging from -10 to 10.  The lines y = x + 3 and y = 3x -4 graphed on the same axes.

Got questions? Get instant answers now!

Chapter practice test

Graph the following: 2 y = 3 x + 4.

y = 3 2 x + 2

x y
0 2
2 5
4 8


A coordinate plane with the x and y axes ranging from -10 to 10.  The line going through the points (0,2); (2,5); and (4,8) is graphed.

Got questions? Get instant answers now!

Find the x- and y -intercepts for the following:

2 x 5 y = 6

Got questions? Get instant answers now!

Find the x- and y -intercepts of this equation, and sketch the graph of the line using just the intercepts plotted.

3 x 4 y = 12

( 0 , −3 ) ( 4 , 0 )


A coordinate plane with the x and y axes ranging from -10 to 10.  The points (4,0) and (0,-3) are plotted with a line running through them.

Got questions? Get instant answers now!

Find the exact distance between ( 5 , −3 ) and ( 2 , 8 ) . Find the coordinates of the midpoint of the line segment joining the two points.

Write the interval notation for the set of numbers represented by { x | x 9 } .

( , 9 ]

Got questions? Get instant answers now!

Solve for x : 5 x + 8 = 3 x 10.

Got questions? Get instant answers now!

Solve for x : 3 ( 2 x 5 ) 3 ( x 7 ) = 2 x 9.

x = −15

Got questions? Get instant answers now!

Solve for x : x 2 + 1 = 4 x

Got questions? Get instant answers now!

Solve for x : 5 x + 4 = 4 + 3 x 2 .

x −4 , 2 ; x = 5 2 , 1

Got questions? Get instant answers now!

The perimeter of a triangle is 30 in. The longest side is 2 less than 3 times the shortest side and the other side is 2 more than twice the shortest side. Find the length of each side.

Got questions? Get instant answers now!

Solve for x . Write the answer in simplest radical form.

x 2 3 x = −1 2

x = 3 ± 3 2

Got questions? Get instant answers now!

Solve: 3 x 8 4.

Got questions? Get instant answers now!

Solve: | 2 x + 3 | < 5.

( −4 , 1 )

Got questions? Get instant answers now!

Solve: | 3 x 2 | 4.

Got questions? Get instant answers now!

For the following exercises, find the equation of the line with the given information.

Passes through the points ( 4 , 2 ) and ( 5 , −3 ) .

y = −5 9 x 2 9

Got questions? Get instant answers now!

Has an undefined slope and passes through the point ( 4 , 3 ) .

Got questions? Get instant answers now!

Passes through the point ( 2 , 1 ) and is perpendicular to y = 2 5 x + 3.

y = 5 2 x 4

Got questions? Get instant answers now!

Add these complex numbers: ( 3 2 i ) + ( 4 i ) .

Got questions? Get instant answers now!

Simplify: −4 + 3 −16 .

14 i

Got questions? Get instant answers now!

Multiply: 5 i ( 5 3 i ) .

Got questions? Get instant answers now!

Divide: 4 i 2 + 3 i .

5 13 14 13 i

Got questions? Get instant answers now!

Solve this quadratic equation and write the two complex roots in a + b i form: x 2 4 x + 7 = 0.

Got questions? Get instant answers now!

Solve: ( 3 x 1 ) 2 1 = 24.

x = 2 , 4 3

Got questions? Get instant answers now!

Solve: x 2 6 x = 13.

Got questions? Get instant answers now!

Solve: 4 x 2 4 x 1 = 0

x = 1 2 ± 2 2

Got questions? Get instant answers now!

Solve:

x 7 = x 7

Got questions? Get instant answers now!

Solve: 2 + 12 2 x = x

4

Got questions? Get instant answers now!

Solve: ( x 1 ) 2 3 = 9

Got questions? Get instant answers now!

For the following exercises, find the real solutions of each equation by factoring.

2 x 3 x 2 8 x + 4 = 0

x = 1 2 , 2 , −2

Got questions? Get instant answers now!

( x + 5 ) 2 3 ( x + 5 ) 4 = 0

Got questions? Get instant answers now!

Questions & Answers

find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
hi
salma
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
Practice Key Terms 4

Get the best College algebra course in your pocket!





Source:  OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College algebra' conversation and receive update notifications?

Ask