<< Chapter < Page Chapter >> Page >

Technology

For the following exercises, input the left-hand side of the inequality as a Y1 graph in your graphing utility. Enter y2 = the right-hand side. Entering the absolute value of an expression is found in the MATH menu, Num, 1:abs(. Find the points of intersection, recall (2 nd CALC 5:intersection, 1 st curve, enter, 2 nd curve, enter, guess, enter). Copy a sketch of the graph and shade the x -axis for your solution set to the inequality. Write final answers in interval notation.

1 2 | x + 2 | < 4

Where the blue is below the orange; always. All real numbers. ( , + ) .


A coordinate plane with the x and y axes ranging from -10 to 10.  The function y = -0.5|x + 2| and the line y = 4 are graphed on the same axes.  A line runs along the entire x-axis.

Got questions? Get instant answers now!

| x 4 | < 3

Where the blue is below the orange; ( 1 , 7 ) .


A coordinate plane with the x and y axes ranging from -10 to 10.  The function y = |x  4| and the line y = 3 are graphed on the same axes.  Along the x-axis the points 1 and 7 have an open circle around them and a line connects the two.

Got questions? Get instant answers now!

Extensions

Solve | 3 x + 1 | = | 2 x + 3 |

x = 2 , 4 5

Got questions? Get instant answers now!

x 5 x + 7 0 , x −7

( −7 , 5 ]

Got questions? Get instant answers now!

p = x 2 + 130 x 3000 is a profit formula for a small business. Find the set of x -values that will keep this profit positive.

Got questions? Get instant answers now!

Real-world applications

In chemistry the volume for a certain gas is given by V = 20 T , where V is measured in cc and T is temperature in ºC. If the temperature varies between 80ºC and 120ºC, find the set of volume values.

80 T 120 1 , 600 20 T 2 , 400

[ 1 , 600 ,   2 , 400 ]

Got questions? Get instant answers now!

A basic cellular package costs $20/mo. for 60 min of calling, with an additional charge of $.30/min beyond that time.. The cost formula would be C = $ 20 + .30 ( x 60 ) . If you have to keep your bill lower than $50, what is the maximum calling minutes you can use?

Got questions? Get instant answers now!

Chapter review exercises

The Rectangular Coordinate Systems and Graphs

For the following exercises, find the x -intercept and the y -intercept without graphing.

4 x 3 y = 12

x -intercept: ( 3 , 0 ) ; y -intercept: ( 0 , −4 )

Got questions? Get instant answers now!

For the following exercises, solve for y in terms of x , putting the equation in slope–intercept form.

5 x = 3 y 12

y = 5 3 x + 4

Got questions? Get instant answers now!

For the following exercises, find the distance between the two points.

( −2 , 5 ) ( 4 , −1 )

72 = 6 2

Got questions? Get instant answers now!

( −12 , −3 ) ( −1 , 5 )

Got questions? Get instant answers now!

Find the distance between the two points ( −71,432 ) and (511,218) using your calculator, and round your answer to the nearest thousandth.

620.097

Got questions? Get instant answers now!

For the following exercises, find the coordinates of the midpoint of the line segment that joins the two given points.

( −1 , 5 )  and  ( 4 , 6 )

Got questions? Get instant answers now!

( −13 , 5 )  and  ( 17 , 18 )

midpoint is ( 2 , 23 2 )

Got questions? Get instant answers now!

For the following exercises, construct a table and graph the equation by plotting at least three points.

4 x 3 y = 6

x y
0 −2
3 2
6 6


A coordinate plane with the x and y axes ranging from -10 to 10.  The points (0,-2); (3,2) and (6,6) are plotted and a line runs through all these points.

Got questions? Get instant answers now!

Linear Equations in One Variable

For the following exercises, solve for x .

3 ( x + 2 ) 10 = x + 4

x = 4

Got questions? Get instant answers now!

12 5 ( x + 1 ) = 2 x 5

x = 12 7

Got questions? Get instant answers now!

2 x 3 3 4 = x 6 + 21 4

Got questions? Get instant answers now!

For the following exercises, solve for x . State all x -values that are excluded from the solution set.

x x 2 9 + 4 x + 3 = 3 x 2 9 x 3 , −3

No solution

Got questions? Get instant answers now!

For the following exercises, find the equation of the line using the point-slope formula.

Passes through these two points: ( −2 , 1 ) , ( 4 , 2 ) .

y = 1 6 x + 4 3

Got questions? Get instant answers now!

Passes through the point ( 3 , 4 ) and has a slope of 1 3 .

Got questions? Get instant answers now!

Passes through the point ( 3 , 4 ) and is parallel to the graph y = 2 3 x + 5.

y = 2 3 x + 6

Got questions? Get instant answers now!

Passes through these two points: ( 5 , 1 ) , ( 5 , 7 ) .

Got questions? Get instant answers now!

Models and Applications

For the following exercises, write and solve an equation to answer each question.

The number of males in the classroom is five more than three times the number of females. If the total number of students is 73, how many of each gender are in the class?

females 17, males 56

Got questions? Get instant answers now!

Questions & Answers

use the properties of logarithms to rewrite as a single logarithmic expression 2+log base 5 t divided by log base 5 17
lucas Reply
Natural numbers of definitions
Ali
(cos²x +tan²x)÷(sec²x+cos²x)
Sonu Reply
Solve the problem 3x^2_2x+4=0
Ayoman Reply
can anyone recommend an app or. website to help me refresh my knowledge and abilities? I stopped learning more about calc and trig in the 90's
scott Reply
if 6x=-2 find value of 6/x
issaya Reply
l don't know
Aman
I don't know
Aman
l don't know
Aman
I don't know
Aman
x=.333333333334, so 6/x= 18±
scott
x=.33333333334± 6/x=18±
scott
that is strange, I don't remember inserting the À. the result I got was x= 3333333334± 6/x=18±
scott
I need glasses
scott
X=(-1÷3) X equals minus one third
Melvin
how can I get the answer if don't know it
Adamma
x=-3
Dani
-18
Nwaneri
if sin15°=√p, express the following in terms of p
Norman Reply
I am learning and does someone have the time to tell me what or where this particular equation would be used?
scott
prove sin²x+cos²x=3+cos4x
Kiddy Reply
the difference between two signed numbers is -8.if the minued is 5,what is the subtrahend
jeramie Reply
the difference between two signed numbers is -8.if the minuend is 5.what is the subtrahend
jeramie
what are odd numbers
micheal Reply
numbers that leave a remainder when divided by 2
Thorben
1,3,5,7,... 99,...867
Thorben
7%2=1, 679%2=1, 866245%2=1
Thorben
the third and the seventh terms of a G.P are 81 and 16, find the first and fifth terms.
Suleiman Reply
if a=3, b =4 and c=5 find the six trigonometric value sin
Martin Reply
ask
Ans
pls how do I factorize x⁴+x³-7x²-x+6=0
Gift Reply
in a function the input value is called
Rimsha Reply
how do I test for values on the number line
Modesta Reply
if a=4 b=4 then a+b=
Rimsha Reply
a+b+2ab
Kin
commulative principle
DIOSDADO
a+b= 4+4=8
Mimi
If a=4 and b=4 then we add the value of a and b i.e a+b=4+4=8.
Tariq
0.2502502
Ali
Practice Key Terms 4

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

Ask