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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

June needs 45 gallons of punch. 2 different coolers. Bigger cooler is 5 times as large as smaller cooler. How many gallons in each cooler?
Arleathia Reply
find the sum of 28th term of the AP 3+10+17+---------
Prince Reply
I think you should say "28 terms" instead of "28th term"
Vedant
if sequence sn is a such that sn>0 for all n and lim sn=0than prove that lim (s1 s2............ sn) ke hole power n =n
SANDESH Reply
write down the polynomial function with root 1/3,2,-3 with solution
Gift Reply
if A and B are subspaces of V prove that (A+B)/B=A/(A-B)
Pream Reply
write down the value of each of the following in surd form a)cos(-65°) b)sin(-180°)c)tan(225°)d)tan(135°)
Oroke Reply
Prove that (sinA/1-cosA - 1-cosA/sinA) (cosA/1-sinA - 1-sinA/cosA) = 4
kiruba Reply
what is the answer to dividing negative index
Morosi Reply
In a triangle ABC prove that. (b+c)cosA+(c+a)cosB+(a+b)cisC=a+b+c.
Shivam Reply
give me the waec 2019 questions
Aaron Reply
the polar co-ordinate of the point (-1, -1)
Sumit Reply
prove the identites sin x ( 1+ tan x )+ cos x ( 1+ cot x )= sec x + cosec x
Rockstar Reply
tanh`(x-iy) =A+iB, find A and B
Pankaj Reply
B=Ai-itan(hx-hiy)
Rukmini
Give me the reciprocal of even number
Aliyu
The reciprocal of an even number is a proper fraction
Jamilu
what is the addition of 101011 with 101010
Branded Reply
If those numbers are binary, it's 1010101. If they are base 10, it's 202021.
Jack
extra power 4 minus 5 x cube + 7 x square minus 5 x + 1 equal to zero
archana 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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