Questions on Algebra: Inequalities, trichotomy answered by real tutors!

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Question 1167831: The product of 4 and a number, decreased by 6, is at least the sum of 8 and twice the number. Write and solve an inequality to find the numbers that satisfy this condition.
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Question 1167834: Dora wants to buy pasta to donate to the school food drive. The average box of pasta costs $1.25 and she needs to purchase a box to put pasta in for $4. Dora only has $15 to spend. How many boxes of pasta can she buy? Write and solve an inequality for this situation.
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Question 1168323:
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Question 1168423: For the function ​g(x)=x+8/x+2, solve the following inequality.
​g(x)>0

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Question 1168619: Graph the solution m<5
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Question 1168629: solve |x+2|<|x-5|
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Question 1168685: The borough of Pan Sherzando charges homeowners $75.24 per month plus $3.86 per
1000 litres for water usage in excess of 10,000 litres. In 2019 one homeowner’s monthly
bill ranged from $137.00 to $245.08. Find the range for the water used by that homeowner

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Question 1168726: The sides of square ABCD are extended to form rectangle DEFG. If the perimeter of the rectangle is at least twice the perimeter of the square, what is the maximum length of a side of square ABCD?
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Question 1169170: Write an inequality that describes the situation.
Your height g has to be at least 48 inches in order to ride the roller coaster.

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Question 1169354: For each of the following, determine whether the statement is sometimes, always, or never true.
x≥1/x(x≠0)


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Question 1169411: You are comparing cell phone plans. Verizon says each phone line is $40 and there is a start up fee of $60. T-Mobile says each line costs $25 and the initial fee is $150. Find the number of phones and the cost each plan will be when the plans cost the same.
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Question 1169706: Can you help me solve this inequality and graph the solution?
2k - 6 > 3k + 2

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Question 1169706: Can you help me solve this inequality and graph the solution?
2k - 6 > 3k + 2

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Question 1169863:
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Question 1170000: what is the equivalent value of the inequalities of x-6<0 ?
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Question 1170194: Based only on the slope of the line fit to the graph of Raven's progressive, which conclusion could Raven's supervisor draw?
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Question 1170188: -5t+6 greater than or equal to -39
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Question 1170131: according to the national center for health statistics, in 1990, 28% of babies in the united states were born to parents who were not married. throughout the 1990s, this increased by approximately 0.6% per year. if this trend continues, in which year will 61% of babies be born out of wedlock
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Question 1170293: The length of the floor is 32m longer than its width and there is more than 200 square meters. You will cover the floor completely with tiles. What will be the possible dimensions of the floor?
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Question 1170293: The length of the floor is 32m longer than its width and there is more than 200 square meters. You will cover the floor completely with tiles. What will be the possible dimensions of the floor?
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Question 1170293: The length of the floor is 32m longer than its width and there is more than 200 square meters. You will cover the floor completely with tiles. What will be the possible dimensions of the floor?
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Question 1170391: Choose a possible dimensions of a rectangle with a width= 2x-1 and length= 3x+2 so that its area is greater than 153cm²
a. W= 13 L= 15
b. W= 11 L= 20
c. W= 11 L= 21
d. W= 13 L= 22
#My answer would be 10cm by 18cm, is it correct? or not?

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Question 1170391: Choose a possible dimensions of a rectangle with a width= 2x-1 and length= 3x+2 so that its area is greater than 153cm²
a. W= 13 L= 15
b. W= 11 L= 20
c. W= 11 L= 21
d. W= 13 L= 22
#My answer would be 10cm by 18cm, is it correct? or not?

Click here to see answer by Clanther(6) About Me 

Question 1170395: If the room has a length of 12m more than its width and an area of more than or equal to 108m², how many tiles to cover completely the room considering that a tile has an area of less than or equal to 1600cm²? What is my preferred budget if one tile cost more or less 56 pesos
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Question 1170817: -12 > x What number is x to make this inequality true?'
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Question 1170831: Solve the following absolute value equations. If there is no solution, write DNE or if all real numbers are solutions, write ARS and explain why. Show all your works (4 points each)
1) |6x| + 12 = 6
2) |2x - 5| - 9 = -2

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Question 1171147: Write and solve an inequality.
School: Logan earned these scores on the first three tests in biology this term: 86, 88, and 78. What is the lowest score that Logan can earn on the fourth and final test of the term if he wants to have an average of at least 83?

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Question 1171293: A polynomial f(x) with real coefficients and leading coefficient 1 has the given zeros and degree. Express f(x) as a product of linear and/or quadratic polynomials with real coefficients that are irreducible over ℝ.
−1, 0, 5 + i; degree 4

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Question 1171293: A polynomial f(x) with real coefficients and leading coefficient 1 has the given zeros and degree. Express f(x) as a product of linear and/or quadratic polynomials with real coefficients that are irreducible over ℝ.
−1, 0, 5 + i; degree 4

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Question 1171351: Jessica runs each lap in 8 minutes. She will run more than 48 minutes today. What are the possible numbers of laps she will run today? Use n for the number of laps she will run today. Write your answer as an inequality solved for n
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Question 1171128: Americans are buying more bottled water than ever before. At the time of this writing, the average American buys more bottled water than milk, coffee, or beer. In 2003, the average American purchased 76.4 gal of soft drinks and water. The amount of water was only 4.3 gal less than half of the amount of soft drinks.

How many gallons of water and how many soft drinks did the average American buy in 2003?

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Question 1171523: Cynthia and Julian have practiced solving inequalities, one of them made a mistake. find out which one made a mistake, and explain where the mistake was made.
Cynthia Julian
n n
_ - 11 > -20 _ + 16 < 15
5 13

n n
_ > -31 _ < -1
5 13
n > -155 n < -13

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Question 1171426: Find a polynomial f(x) of degree 3 that has the indicated zeros and satisfies
the given condition.
−4i, 4i, 2; f(1) = 51

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Question 1171521: Jamal works in a city and
sometimes takes a taxi to work. The
taxicabs charge $1.50 for the first −1 mile 15
and $0.25 for each additional −5 mile.
Jamal has only $3.75 in his pocket. What is the maximum distance he can travel by cab if he does not intend to tip the cab driver?

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Question 1172200: Tell whether the given number can be a solution of 5x-10 > 2x+4. The given
number is 4.

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Question 1172200: Tell whether the given number can be a solution of 5x-10 > 2x+4. The given
number is 4.

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Question 1172392: Fins the solution set of the inequality 1/(x - 2) < 1/(x + 3)?
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Question 1172573: The Instructions: Solve this word problem using an inequality. Express the answer as an inequality. Show your work.
The Problem: Gary wants to buy a computer that costs $645. He earns about $10 per hour at his new job after taxes are deducted from his paycheck. At least how many hours does he have to work before he can buy the computer?
What I did:
$10 (x) = $645
I divided $10 by $10 and cancelled it out on the left side, then I divided $645 by $10.
I got 64.5 and wasn't sure if I should round or not.
x = 64.5
Then I thought about using ≥.
$10 (x) ≥ $645
I did the same thing I did before and got
x ≥ 64.5
Then I rounded up to get this.
x ≥ 65
I'm not sure if I'm allowed to round. It didn't tell me to, but I'm not sure if it's something that's assumed, could you please help me figure this out?

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Question 1172617: x+4y=8
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Question 1172623: A school has a budget of Php7,000 per section to buy workbooks. A Math workbook costs Php 160.00, and a Science workbook costs Pho 175.00. If you want to buy 20 Science workbooks, what is the maximum number of Math workbooks can you buy?
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Question 1172689: Verify if the given ordered pair is a solution of the inequality
1. x- 3y ≤ - 6 ; a. (4,5) b.(-1,-2)
2. 5x + 2y ≥ 11 ; a. (1,2) b.(3,-4)

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Question 1172732: what happens when you multiply or divide by a negative number when working with inequalities?
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Question 1172729: 2. The 9th grade class has decided that they want to go on a trip to Six Flags Great Adventure. Each section has to fundraise for themselves in order to get the money to go. In Section A, there are 25 students. If the cost of a ticket and the bus ride are combined, they will cost $35 per student. Section A has decided that they want to have a bake sale to raise some money. They were given a donation of cakes, cookies, and soda by parents so no money was spent on supplies. How many of each item will need to be sold in order to raise at least enough money to go on the trip? Come up with possible solutions for this problem!
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Question 1172837: what is p is within 0.0004 units of 2
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Question 1172837: what is p is within 0.0004 units of 2
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205