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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.

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| 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.

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Extensions

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

x = 2 , 4 5

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x 5 x + 7 0 , x −7

( −7 , 5 ]

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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.

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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 ]

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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?

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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 )

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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

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

( −2 , 5 ) ( 4 , −1 )

72 = 6 2

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( −12 , −3 ) ( −1 , 5 )

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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

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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 )

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( −13 , 5 )  and  ( 17 , 18 )

midpoint is ( 2 , 23 2 )

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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.

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Linear Equations in One Variable

For the following exercises, solve for x .

3 ( x + 2 ) 10 = x + 4

x = 4

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12 5 ( x + 1 ) = 2 x 5

x = 12 7

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2 x 3 3 4 = x 6 + 21 4

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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

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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

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

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

y = 2 3 x + 6

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

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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

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Questions & Answers

Find the possible value of 8.5 using moivre's theorem
Reuben Reply
which of these functions is not uniformly cintinuous on (0, 1)? sinx
Pooja Reply
which of these functions is not uniformly continuous on 0,1
Basant Reply
solve this equation by completing the square 3x-4x-7=0
Jamiz Reply
X=7
Muustapha
=7
mantu
x=7
mantu
3x-4x-7=0 -x=7 x=-7
Kr
x=-7
mantu
9x-16x-49=0 -7x=49 -x=7 x=7
mantu
what's the formula
Modress
-x=7
Modress
what is trigonometry
Jean Reply
deals with circles, angles, and triangles. Usually in the form of Soh cah toa or sine, cosine, and tangent
Thomas
solve for me this equational y=2-x
Rubben Reply
what are you solving for
Alex
solve x
Rubben
you would move everything to the other side leaving x by itself. subtract 2 and divide -1.
Nikki
then I got x=-2
Rubben
it will b -y+2=x
Alex
goodness. I'm sorry. I will let Alex take the wheel.
Nikki
ouky thanks braa
Rubben
I think he drive me safe
Rubben
how to get 8 trigonometric function of tanA=0.5, given SinA=5/13? Can you help me?m
Pab Reply
More example of algebra and trigo
Stephen Reply
What is Indices
Yashim Reply
If one side only of a triangle is given is it possible to solve for the unkown two sides?
Felix Reply
cool
Rubben
kya
Khushnama
please I need help in maths
Dayo Reply
Okey tell me, what's your problem is?
Navin
the least possible degree ?
Dejen Reply
(1+cosA)(1-cosA)=sin^2A
BINCY Reply
good
Neha
why I'm sending you solved question
Mirza
Teach me abt the echelon method
Khamis
exact value of cos(π/3-π/4)
Ankit Reply
What is differentiation?
Intakhab Reply
Practice Key Terms 4

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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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