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?

  • Aโˆ’9
  • Bโˆ’4
  • Cโˆ’2
  • Dโˆ’8

Q5:

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

  • A๐‘ฅ>โˆ’28
  • B๐‘ฅ<โˆ’28
  • Cโˆ’๐‘ฅโ‰ฅ28
  • Dโˆ’๐‘ฅ<โˆ’28

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?

  • A๐‘ฅ>51
  • B๐‘ฅ<51
  • Cโˆ’๐‘ฅ>52
  • Dโˆ’๐‘ฅ>โˆ’52

Q8:

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

  • A๐‘ฅ>2
  • Bโˆ’๐‘ฅ>4
  • C๐‘ฅ<2
  • Dโˆ’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.

  • Aโ‰ฅ
  • B>
  • C=
  • D<

Q13:

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

  • A๐‘Ž+๐‘>๐‘+๐‘
  • B๐‘Ž+๐‘โ‰ฅ๐‘+๐‘
  • C๐‘Žร—๐‘>๐‘ร—๐‘
  • D๐‘Žร—๐‘โ‰ฅ๐‘
  • E๐‘Žร—๐‘โ‰ฅ๐‘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?

  • A๐‘ฅ>9๐‘ฅ๏Šจ
  • B๐‘ฅโ‰ฅ9๐‘ฅ๏Šจ
  • C๐‘ฅโ‰ค9๐‘ฅ๏Šจ
  • D๐‘ฅ<9๐‘ฅ๏Šจ
  • E๐‘ฅ=9๐‘ฅ๏Šจ

Q16:

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

  • A5๐‘ฅ<9๐‘ฆ
  • B5๐‘ฅ=9๐‘ฆ
  • C5๐‘ฅโ‰ฅ9๐‘ฆ
  • D5๐‘ฅโ‰ค9๐‘ฆ
  • E5๐‘ฅ>9๐‘ฆ

Q17:

Which of the following inequalities is true?

  • Aโˆ’25<0<โˆ’1
  • B0<โˆ’25<โˆ’1
  • Cโˆ’1<0<โˆ’25
  • Dโˆ’1<โˆ’25<0
  • Eโˆ’25<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?

  • Aโˆ’1.4>โˆ’1.32>0
  • B0>โˆ’1.32>โˆ’1.4
  • C0>โˆ’1.4>โˆ’1.32
  • Dโˆ’1.4>0>โˆ’1.32
  • Eโˆ’1.32>โˆ’1.4>0

Q20:

Which of the following inequalities is true?

  • Aโˆ’15.5<โˆ’14.75<โˆ’15.25
  • Bโˆ’14.75<โˆ’15.5<โˆ’15.25
  • Cโˆ’14.75<โˆ’15.25<โˆ’15.5
  • Dโˆ’15.25<โˆ’15.5<โˆ’14.75
  • Eโˆ’15.5<โˆ’15.25<โˆ’14.75

Q21:

Which of the following inequalities is true?

  • Aโˆ’7.4>โˆ’7.15>โˆ’7.28
  • Bโˆ’7.15>โˆ’7.4>โˆ’7.28
  • Cโˆ’7.15>โˆ’7.28>โˆ’7.4
  • Dโˆ’7.28>โˆ’7.15>โˆ’7.4
  • Eโˆ’7.4>โˆ’7.28>โˆ’7.15

Q22:

Which of the following inequalities is true?

  • Aโˆ’8<โˆ’15<0<8<15
  • B0<โˆ’8<8<โˆ’15<15
  • Cโˆ’15<โˆ’8<0<8<15
  • Dโˆ’15<โˆ’8<0<15<8
  • Eโˆ’8<โˆ’15<0<15<8

Q23:

Which of the following inequalities is true?

  • A22>โˆ’22>17>โˆ’17>0
  • Bโˆ’22>โˆ’17>0>17>22
  • C22>17>0>โˆ’22>โˆ’17
  • D22>17>0>โˆ’17>โˆ’22
  • E22>17>โˆ’17>โˆ’22>0

Q24:

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

  • Aโˆ’10
  • Bโˆ’5
  • Cโˆ’9
  • Dโˆ’11

Q25:

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

  • Aโˆ’4
  • Bโˆ’1
  • C2
  • Dโˆ’3

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