Worksheet: Determining Whether an Inequality Is True or False

In this worksheet, we will practice knowing whether an inequality is true or false for a given value of a variable and determining numbers that satisfy an inequality.

Q1:

Given that ๐‘=11, is the inequality 28โˆ’๐‘<34 true or false?

  • Afalse
  • Btrue

Q2:

Is the inequality 15ร—๐‘ฆโ‰ค93รท3 true or false if ๐‘ฆ=2?

  • Afalse
  • Btrue

Q3:

Given that ๐‘š=11, is the inequality 8๐‘šโ‰ค64 true or false?

  • Atrue
  • Bfalse

Q4:

Which of the following values of ๐‘ฅ does NOT satisfy the inequality ๐‘ฅ>โˆ’9?

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

Q5:

Which of the following inequalities does the number โˆ’28 satisfy?

  • A ๐‘ฅ > โˆ’ 2 8
  • B ๐‘ฅ < โˆ’ 2 8
  • C โˆ’ ๐‘ฅ โ‰ฅ 2 8
  • D โˆ’ ๐‘ฅ < โˆ’ 2 8

Q6:

Choose the largest integer below which satisfies the inequality ๐‘ฅ>6.

  • A4
  • B5
  • C9
  • D6
  • E8

Q7:

Which of the following inequalities has ๐‘ฅ=51 as a solution?

  • A ๐‘ฅ > 5 1
  • B ๐‘ฅ < 5 1
  • C โˆ’ ๐‘ฅ > 5 2
  • D โˆ’ ๐‘ฅ > โˆ’ 5 2

Q8:

The number 2 is a solution to which one of these inequalities?

  • A ๐‘ฅ > 2
  • B โˆ’ ๐‘ฅ > 4
  • C ๐‘ฅ < 2
  • D โˆ’ ๐‘ฅ > โˆ’ 4

Q9:

State whether the following is true or false: If ๐‘Ž and ๐‘ belong to โ„ and ๐‘Ž>๐‘, where ๐‘Ž and ๐‘ have the same signs, then 1๐‘Ž<1๐‘.

  • Afalse
  • Btrue

Q10:

Complete the statement: The greatest integer that satisfies the inequality 0<๐‘ฅ<3 is .

Q11:

Which of the following points is not a solution of the inequality โˆ’3๐‘ฅโˆ’3๐‘ฆโ‰ค5?

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

Q12:

Which of the relation symbols below makes the following statement true? The point (โˆ’3,2) belongs to the solution set of the inequality 4๐‘ฅ+2๐‘ฆโˆ’2.

  • A โ‰ฅ
  • B >
  • C =
  • D <

Q13:

If ๐‘Žโ‰ฅ๐‘ and ๐‘<0, which of the following inequalities is true?

  • A ๐‘Ž + ๐‘ > ๐‘ + ๐‘
  • B ๐‘Ž + ๐‘ โ‰ฅ ๐‘ + ๐‘
  • C ๐‘Ž ร— ๐‘ > ๐‘ ร— ๐‘
  • D ๐‘Ž ร— ๐‘ โ‰ฅ ๐‘
  • E ๐‘Ž ร— ๐‘ โ‰ฅ ๐‘ ร— ๐‘

Q14:

Which of the following points belongs to the solution set of the inequality 8๐‘ฅ+3๐‘ฆโ‰ฅโˆ’7?

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

Q15:

Which of the following are true given that 0<๐‘ฅ<9?

  • A ๐‘ฅ > 9 ๐‘ฅ ๏Šจ
  • B ๐‘ฅ โ‰ฅ 9 ๐‘ฅ ๏Šจ
  • C ๐‘ฅ โ‰ค 9 ๐‘ฅ ๏Šจ
  • D ๐‘ฅ < 9 ๐‘ฅ ๏Šจ
  • E ๐‘ฅ = 9 ๐‘ฅ ๏Šจ

Q16:

If ๐‘ฅโˆˆโ„๏Šฐ, ๐‘ฆโˆˆโ„๏Šฐ, and 25๐‘ฅ<81๐‘ฆ๏Šจ๏Šจ, which of the following is true?

  • A 5 ๐‘ฅ < 9 ๐‘ฆ
  • B 5 ๐‘ฅ = 9 ๐‘ฆ
  • C 5 ๐‘ฅ โ‰ฅ 9 ๐‘ฆ
  • D 5 ๐‘ฅ โ‰ค 9 ๐‘ฆ
  • E 5 ๐‘ฅ > 9 ๐‘ฆ

Q17:

Which of the following inequalities is true?

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

Q18:

Is the inequality 3<8โˆ’๐‘ฅ true or false if ๐‘ฅ=5?

  • Atrue
  • Bfalse

Q19:

Which of the following inequalities is true?

  • A โˆ’ 1 . 4 > โˆ’ 1 . 3 2 > 0
  • B 0 > โˆ’ 1 . 3 2 > โˆ’ 1 . 4
  • C 0 > โˆ’ 1 . 4 > โˆ’ 1 . 3 2
  • D โˆ’ 1 . 4 > 0 > โˆ’ 1 . 3 2
  • E โˆ’ 1 . 3 2 > โˆ’ 1 . 4 > 0

Q20:

Which of the following inequalities is true?

  • A โˆ’ 1 5 . 5 < โˆ’ 1 4 . 7 5 < โˆ’ 1 5 . 2 5
  • B โˆ’ 1 4 . 7 5 < โˆ’ 1 5 . 5 < โˆ’ 1 5 . 2 5
  • C โˆ’ 1 4 . 7 5 < โˆ’ 1 5 . 2 5 < โˆ’ 1 5 . 5
  • D โˆ’ 1 5 . 2 5 < โˆ’ 1 5 . 5 < โˆ’ 1 4 . 7 5
  • E โˆ’ 1 5 . 5 < โˆ’ 1 5 . 2 5 < โˆ’ 1 4 . 7 5

Q21:

Which of the following inequalities is true?

  • A โˆ’ 7 . 4 > โˆ’ 7 . 1 5 > โˆ’ 7 . 2 8
  • B โˆ’ 7 . 1 5 > โˆ’ 7 . 4 > โˆ’ 7 . 2 8
  • C โˆ’ 7 . 1 5 > โˆ’ 7 . 2 8 > โˆ’ 7 . 4
  • D โˆ’ 7 . 2 8 > โˆ’ 7 . 1 5 > โˆ’ 7 . 4
  • E โˆ’ 7 . 4 > โˆ’ 7 . 2 8 > โˆ’ 7 . 1 5

Q22:

Which of the following inequalities is true?

  • A โˆ’ 8 < โˆ’ 1 5 < 0 < 8 < 1 5
  • B 0 < โˆ’ 8 < 8 < โˆ’ 1 5 < 1 5
  • C โˆ’ 1 5 < โˆ’ 8 < 0 < 8 < 1 5
  • D โˆ’ 1 5 < โˆ’ 8 < 0 < 1 5 < 8
  • E โˆ’ 8 < โˆ’ 1 5 < 0 < 1 5 < 8

Q23:

Which of the following inequalities is true?

  • A 2 2 > โˆ’ 2 2 > 1 7 > โˆ’ 1 7 > 0
  • B โˆ’ 2 2 > โˆ’ 1 7 > 0 > 1 7 > 2 2
  • C 2 2 > 1 7 > 0 > โˆ’ 2 2 > โˆ’ 1 7
  • D 2 2 > 1 7 > 0 > โˆ’ 1 7 > โˆ’ 2 2
  • E 2 2 > 1 7 > โˆ’ 1 7 > โˆ’ 2 2 > 0

Q24:

Which one of the following numbers satisfies the inequality ๐‘ฅ>โˆ’6?

  • A โˆ’ 1 0
  • B โˆ’ 5
  • C โˆ’ 9
  • D โˆ’ 1 1

Q25:

Which of the following does not satisfy the inequality ๐‘ฅโ‰คโˆ’1?

  • A โˆ’ 4
  • B โˆ’ 1
  • C2
  • D โˆ’ 3

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