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Worksheet: Determining Whether an Inequality Is True or False

Q1:

Given that 𝑏 = 1 1 , is the inequality 2 8 βˆ’ 𝑏 < 3 4 true or false?

  • Atrue
  • Bfalse

Q2:

Is the inequality true or false if 𝑦 = 2 ?

  • Atrue
  • Bfalse

Q3:

Complete the statement: The greatest integer that satisfies the inequality 0 < π‘₯ < 3 is .

Q4:

Which of the following inequalities is true?

  • A 0 < βˆ’ 2 5 < βˆ’ 1
  • B βˆ’ 2 5 < βˆ’ 1 < 0
  • C βˆ’ 1 < 0 < βˆ’ 2 5
  • D βˆ’ 1 < βˆ’ 2 5 < 0
  • E βˆ’ 2 5 < 0 < βˆ’ 1

Q5:

Which of the following are true given that 0 < π‘₯ < 9 ?

  • A π‘₯ > 9 π‘₯ 2
  • B π‘₯ = 9 π‘₯ 2
  • C π‘₯ ≀ 9 π‘₯ 2
  • D π‘₯ < 9 π‘₯ 2
  • E π‘₯ β‰₯ 9 π‘₯ 2

Q6:

Which of the following points is not a solution of the inequality βˆ’ 3 π‘₯ βˆ’ 3 𝑦 ≀ 5 ?

  • A ( βˆ’ 5 , 8 )
  • B ( 8 , 0 )
  • C ( 6 , 3 )
  • D ( βˆ’ 1 , βˆ’ 4 )
  • E ( 6 , 0 )

Q7:

Which of the relation symbols below makes the following statement true? The point ( βˆ’ 3 , 2 ) belongs to the solution set of the inequality 4 π‘₯ + 2 𝑦 βˆ’ 2 .

  • A >
  • B β‰₯
  • C =
  • D <

Q8:

If π‘Ž β‰₯ 𝑏 and 𝑐 < 0 , which of the following inequalities is true?

  • A π‘Ž Γ— 𝑐 β‰₯ 𝑏 Γ— 𝑐
  • B π‘Ž + 𝑐 > 𝑏 + 𝑐
  • C π‘Ž Γ— 𝑐 > 𝑏 Γ— 𝑐
  • D π‘Ž + 𝑐 β‰₯ 𝑏 + 𝑐
  • E π‘Ž Γ— 𝑏 β‰₯ 𝑐

Q9:

Which of the following inequalities does the number βˆ’ 2 8 satisfy?

  • A π‘₯ > βˆ’ 2 8
  • B βˆ’ π‘₯ < βˆ’ 2 8
  • C π‘₯ < βˆ’ 2 8
  • D βˆ’ π‘₯ β‰₯ 2 8

Q10:

Which of the following points belongs to the solution set of the inequality βˆ’ π‘₯ βˆ’ 9 𝑦 ≀ βˆ’ 3 ?

  • A ( 8 , βˆ’ 2 )
  • B ( 3 , βˆ’ 9 )
  • C ( 3 , βˆ’ 1 )
  • D ( βˆ’ 6 , 9 )
  • E ( 5 , βˆ’ 1 )

Q11:

Choose the largest integer below which satisfies the inequality π‘₯ > 6 .

  • A 4
  • B 8
  • C 5
  • D 9
  • E 6

Q12:

If π‘₯ ∈ ℝ + , 𝑦 ∈ ℝ + , and 2 5 π‘₯ < 8 1 𝑦 2 2 , which of the following is true?

  • A 5 π‘₯ = 9 𝑦
  • B 5 π‘₯ > 9 𝑦
  • C 5 π‘₯ β‰₯ 9 𝑦
  • D 5 π‘₯ < 9 𝑦
  • E 5 π‘₯ ≀ 9 𝑦

Q13:

Given that π‘š = 5 , is the inequality 4 0 π‘š ≀ 2 6 true or false?

  • Atrue
  • Bfalse

Q14:

Given that π‘š = 1 9 , is the inequality βˆ’ 3 π‘š ≀ 7 4 true or false?

  • Atrue
  • Bfalse

Q15:

Given that π‘š = 1 1 , is the inequality 8 π‘š ≀ 6 4 true or false?

  • Afalse
  • Btrue

Q16:

State whether the following is true or false: If π‘Ž and 𝑏 belong to ℝ and π‘Ž > 𝑏 , where π‘Ž and 𝑏 have the same signs, then 1 π‘Ž < 1 𝑏 .

  • Atrue
  • Bfalse

Q17:

Which of the following values of π‘₯ does NOT satisfy the inequality π‘₯ > βˆ’ 9 ?

  • A βˆ’ 4
  • B βˆ’ 8
  • C βˆ’ 2
  • D βˆ’ 9

Q18:

Is the inequality true or false if π‘₯ = 5 ?

  • Afalse
  • Btrue

Q19:

What is the name of the set of all values that satisfy a given equation or inequality?

  • Athe satisfaction set
  • Bthe substitution set
  • Cthe solving set
  • Dthe solution set
  • Ethe data set