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Yaadannoo boqonnaa fi gaaffii shaakalaa

Boqonnaa 4 Herrega kutaa 9: Walqixxummaa-dhabeeyyii Hiikuu

Wanti fuula kana irra jiru hundi boqonnaa 4 kitaaba Herrega kutaa 9 tiif: wanta boqonnaan haguugu, yaadannoo gabaabaa, gaaffii shaakalaa deebii isaanii waliin, fi viidiyoo barnootaa bakka jirutti.

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5
Kaardii
10
Gaaffii shaakalaa boqonnaa 4
130–161
Fuula kitaabaa boqonnaa 4

Boqonnaan 4 maal haguuga

  1. 1.Revision on Linear Inequalities in One Variable
  2. 2.Systems of Linear Inequalities in Two Variables
  3. 3.Inequalities Involving Absolute Value
  4. 4.Quadratic Inequalities
  5. 5.Applications

Yaadannoo gabaabaa boqonnaa 4

Kaardiiwwan fuula Herrega kutaa 9 irratti boqonnaa kana jala galmaa'an. Tokko tokkoon bani.

∣k∣<c  ⟺  −c<k<cand∣k∣>c  ⟺  k>c or k<−c|k| < c \iff -c < k < c \quad \text{and} \quad |k| > c \iff k > c \text{ or } k < -c
kk
himmannoo aljebraadimensionlessdimensionless
cc
dhaabbataa lakkoofsa poozatiiviidimensionlessdimensionless

Yoom akka itti fayyadamtu

Walsimbiroo dhabuu sararaawaa gatii cimaa of keessaa qabu furuuf fayyadami.

Of eeggadhu

Gatii cimaa isa mallattoo irra caalaa qabu gara qooda lamaatti osoo hin baasin akka tokkootti furuun dogoggora fida.

Grade 9 Mathematics, fuula 130-161 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Yoom akka itti fayyadamtu

Dirree furmaata walsimbiroo dhabuu sararaawaa diriira koordinetii irratti argachuuf fayyadami.

Of eeggadhu

Qabxii qormaatichaa sarara daangaa irratti filachuun gama isa kam akka halluu dibdu hin beeksisu.

Grade 9 Mathematics, fuula 130-161 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

GaraagarummaaWalsimbiroo dhabuuQabxiiwwan Daangaa
(a,b)(a, b)a<x<ba < x < bOpen dots at aa and bb
[a,b][a, b]a≤x≤ba \le x \le bSolid dots at aa and bb
(a,b](a, b]a<x≤ba < x \le bOpen dot at aa, solid dot at bb
[a,b)[a, b)a≤x<ba \le x < bSolid dot at aa, open dot at bb

Yoom akka itti fayyadamtu

Tuuta furmaata walsimbiroo dhabuu sarara lakkoofsaa irratti yookiin bifa garaagarummaatiin ibsuuf fayyadami.

Of eeggadhu

Walsimbiroo dhabuu jabaa hin taaneef qabxii banaa fayyadamuun qabxii daangaa sirrii dhabsiisa.

Grade 9 Mathematics, fuula 130-161 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Yoom akka itti fayyadamtu

Gara lamaan walsimbiroo dhabuu lakkoofsa negatiiviin yeroo baayiftu yookiin hirtu fayyadami.

Of eeggadhu

Lakkoofsa negatiiviin yeroo baayiftu yookiin hirtu mallattoo walsimbiroo dhabuu garagalchuu dhiisuun deebii dogoggoraa kenna.

Grade 9 Mathematics, fuula 130-161 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Yoom akka itti fayyadamtu

Walsimbiroo dhabuu kooridiraatikii bifa baayataan jiru zeeroo irra caaluu yookiin xiqqaachuu isaa furuuf fayyadami.

Of eeggadhu

Baayataan negatiivii yeroo ta'u lameen isaaniiyyuu mallattoo waloo qabu jedhanii yaaduun dogoggora. Mallattoo faallaa qabaachuu qabu.

Grade 9 Mathematics, fuula 130-161 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Gaaffii shaakalaa boqonnaa 4

Gaaffii filannoo 10 boqonnaa kana irratti barreeffaman, tokkoon tokkoon isaanii deebii fi sababa qabu. Deebii banuu dura yaali. Gaaffiin kun Ingiliffaa tiin.

Gaaffii 1

According to the properties of inequalities, if a > b and m < 0, which of the following is true?

  1. A.ma > mb
  2. B.ma < mb
  3. C.a + m < b + m
  4. D.a - m < b - m
Deebii fi sababa agarsiisi

Deebii: B ma < mb

Sababa

When both sides of an inequality are multiplied or divided by a negative number, the direction of the inequality sign is reversed. Since m < 0, multiplying a > b by m gives ma < mb.

Gaaffii 2

Which interval notation represents the set of all real numbers x such that -3 ≤ x < 2?

  1. A.[-3, 2]
  2. B.(-3, 2]
  3. C.[-3, 2)
  4. D.(-3, 2)
Deebii fi sababa agarsiisi

Deebii: C [-3, 2)

Sababa

A square bracket is used for included endpoints (≤ or ≥) and a round parenthesis is used for excluded endpoints (< or >). Therefore, -3 ≤ x < 2 is written as [-3, 2).

Gaaffii 3

What is the solution set of the absolute value inequality |6x + 8| > -2?

  1. A.No solution
  2. B.x > -1
  3. C.x < -1
  4. D.All real numbers
Deebii fi sababa agarsiisi

Deebii: D All real numbers

Sababa

The absolute value of any real number is always non-negative (greater than or equal to 0). Since 0 is always greater than -2, the inequality holds true for all real numbers.

Gaaffii 4

Solve the linear inequality 3x - 9 > 7x - 1.

  1. A.x > -2
  2. B.x < -2
  3. C.x < 2
  4. D.x > 2
Deebii fi sababa agarsiisi

Deebii: B x < -2

Sababa

Subtract 7x from both sides: -4x - 9 > -1. Add 9 to both sides: -4x > 8. Dividing both sides by -4 reverses the inequality symbol, giving x < -2.

Gaaffii 5

What is the solution of the absolute value inequality |x + 2| < 4?

  1. A.-6 < x < 2
  2. B.x < -6 or x > 2
  3. C.-2 < x < 6
  4. D.x > -6
Deebii fi sababa agarsiisi

Deebii: A -6 < x < 2

Sababa

Using the theorem for |k| < c, we write -4 < x + 2 < 4. Subtracting 2 from all parts gives -4 - 2 < x < 4 - 2, which simplifies to -6 < x < 2.

Gaaffii 6

What is the solution in interval notation for the quadratic inequality (x - 3)(x - 1) < 0?

  1. A.(-infinity, 1) U (3, infinity)
  2. B.(1, 3)
  3. C.[-1, 3]
  4. D.(-3, -1)
Deebii fi sababa agarsiisi

Deebii: B (1, 3)

Sababa

For the product of two factors to be negative, one factor must be positive and the other negative. This occurs when x - 1 > 0 and x - 3 < 0, which gives 1 < x < 3, or the interval (1, 3).

Gaaffii 7

What is the solution to the absolute value inequality |-5x - 7| ≤ 0?

  1. A.No solution
  2. B.All real numbers
  3. C.x = 7/5
  4. D.x = -7/5
Deebii fi sababa agarsiisi

Deebii: D x = -7/5

Sababa

An absolute value cannot be strictly less than 0, so the inequality only holds when |-5x - 7| = 0. Solving -5x - 7 = 0 gives -5x = 7, so x = -7/5.

Gaaffii 8

What is the solution set of the quadratic inequality x2 - x ≥ 12?

  1. A.[-3, 4]
  2. B.(-infinity, -4] U [3, infinity)
  3. C.(-infinity, -3] U [4, infinity)
  4. D.[-4, 3]
Deebii fi sababa agarsiisi

Deebii: C (-infinity, -3] U [4, infinity)

Sababa

Rewrite as x2 - x - 12 ≥ 0 and factor to get (x - 4)(x + 3) ≥ 0. The product is non-negative when x ≤ -3 or x ≥ 4, which is (-∞, -3] ∪ [4, ∞).

Gaaffii 9

Kebede has saved 6,000 birr for a tractor. He plans to save 1,000 birr each month until his total savings are more than 80,000 birr. If m is the number of months, which inequality and solution represent his saving plan?

  1. A.6,000 + 1,000m > 80,000; m > 74
  2. B.6,000 + 1,000m <= 80,000; m <= 74
  3. C.1,000m - 6,000 > 80,000; m > 86
  4. D.6,000 + 1,000m >= 80,000; m >= 80
Deebii fi sababa agarsiisi

Deebii: A 6,000 + 1,000m > 80,000; m > 74

Sababa

Kebede starts with 6,000 birr and adds 1,000m birr. To have more than 80,000 birr: 6,000 + 1,000m > 80,000. Subtracting 6,000 gives 1,000m > 74,000, so m > 74.

Gaaffii 10

Chaltu has 50 birr in her phone account. She is charged 0.20 birr for each text message. If her total bill can be at most 80 birr, what is the maximum number of text messages she can send?

  1. A.300
  2. B.150
  3. C.400
  4. D.120
Deebii fi sababa agarsiisi

Deebii: B 150

Sababa

At most means less than or equal to: 0.2m + 50 ≤ 80. Subtracting 50 gives 0.2m ≤ 30. Dividing by 0.2 gives m ≤ 150, so she can send a maximum of 150 messages.

Viidiyoo barnootaa boqonnaa 4

Barnoota boqonnaa kanaa YouTube irraa. Yommuu play tuqxu qofa fe'ama.

Compound inequalities: Linear inequalities (part 2) · YouTube irratti ilaali

Fuula kitaabaa boqonnaa 4

Boqonnaan 4 Maxxansa Ministeera Barnootaa keessatti fuula 130 hanga fuula 161 ti.

Maxxansa Ministeera Barnootaa, Ingiliffaa, Fuula 337

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