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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

the gradient function of a curve is 2x+4 and the curve passes through point (1,4) find the equation of the curve
Kc Reply
1+cos²A/cos²A=2cosec²A-1
Ramesh Reply
test for convergence the series 1+x/2+2!/9x3
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a man walks up 200 meters along a straight road whose inclination is 30 degree.How high above the starting level is he?
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100 meters
Kuldeep
Find that number sum and product of all the divisors of 360
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answer
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exponential series
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what is subgroup
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Prove that: (2cos&+1)(2cos&-1)(2cos2&-1)=2cos4&+1
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e power cos hyperbolic (x+iy)
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10y
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tan hyperbolic inverse (x+iy)=alpha +i bita
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prove that cos(π/6-a)*cos(π/3+b)-sin(π/6-a)*sin(π/3+b)=sin(a-b)
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why {2kπ} union {kπ}={kπ}?
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why is {2kπ} union {kπ}={kπ}? when k belong to integer
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if 9 sin theta + 40 cos theta = 41,prove that:41 cos theta = 41
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what is complex numbers
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Solve 2cos x + 3sin x = 0.5
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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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