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

  • Atrue
  • Bfalse

Q2:

Is the inequality true or false if 𝑦 = 2 ?

  • Atrue
  • Bfalse

Q3:

Given that 𝑚 = 1 1 , is the inequality 8 𝑚 6 4 true or false?

  • Afalse
  • Btrue

Q4:

Which of the following values of 𝑥 does NOT satisfy the inequality 𝑥 > 9 ?

  • A 4
  • B 8
  • C 2
  • D 9

Q5:

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

  • A 𝑥 > 2 8
  • B 𝑥 < 2 8
  • C 𝑥 < 2 8
  • D 𝑥 2 8

Q6:

Choose the largest integer below which satisfies the inequality 𝑥 > 6 .

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

Q7:

Which of the following inequalities has 𝑥 = 5 1 as a solution?

  • A 𝑥 < 5 1
  • B 𝑥 > 5 1
  • C 𝑥 > 5 2
  • D 𝑥 > 5 2

Q8:

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

  • A 𝑥 < 2
  • B 𝑥 > 2
  • C 𝑥 > 4
  • D 𝑥 > 4

Q9:

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

  • Atrue
  • Bfalse

Q10:

Complete the statement: The greatest integer that satisfies the inequality 0 < 𝑥 < 3 is .

Q11:

Which of the following points is not a solution of the inequality 3 𝑥 3 𝑦 5 ?

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

Q12:

Which of the relation symbols below makes the following statement true? The point ( 3 , 2 ) belongs to the solution set of the inequality 4 𝑥 + 2 𝑦 2 .

  • A >
  • B
  • C =
  • D <

Q13:

If 𝑎 𝑏 and 𝑐 < 0 , which of the following inequalities is true?

  • A 𝑎 × 𝑐 𝑏 × 𝑐
  • B 𝑎 + 𝑐 > 𝑏 + 𝑐
  • C 𝑎 × 𝑐 > 𝑏 × 𝑐
  • D 𝑎 + 𝑐 𝑏 + 𝑐
  • E 𝑎 × 𝑏 𝑐

Q14:

Which of the following points belongs to the solution set of the inequality 8 𝑥 + 3 𝑦 7 ?

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

Q15:

Which of the following are true given that 0 < 𝑥 < 9 ?

  • A 𝑥 > 9 𝑥
  • B 𝑥 = 9 𝑥
  • C 𝑥 9 𝑥
  • D 𝑥 < 9 𝑥
  • E 𝑥 9 𝑥

Q16:

If 𝑥 , 𝑦 , and 2 5 𝑥 < 8 1 𝑦 , which of the following is true?

  • A 5 𝑥 = 9 𝑦
  • B 5 𝑥 > 9 𝑦
  • C 5 𝑥 9 𝑦
  • D 5 𝑥 < 9 𝑦
  • E 5 𝑥 9 𝑦

Q17:

Which of the following inequalities is true?

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

Q18:

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

Q19:

Is the inequality true or false if 𝑥 = 5 ?

  • Afalse
  • Btrue

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