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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

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
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Source:  OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
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