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Worksheet: Solving Inequalities by Multiplication or Division

Q1:

Solve 5 π‘₯ > 4 5 for π‘₯ .

  • A π‘₯ = 9
  • B π‘₯ < 9
  • C π‘₯ > 4 0
  • D π‘₯ > 9
  • E π‘₯ = 4 0

Q2:

If βˆ’ 4 2 π‘₯ < βˆ’ 4 1 , then .

  • A π‘₯ < 4 1 4 2
  • B π‘₯ > βˆ’ 4 1 4 2
  • C π‘₯ < βˆ’ 4 1 4 2
  • D π‘₯ > 4 1 4 2

Q3:

Solve the following inequality: 1 4 < 4 9 𝑦 .

  • A 1 9 < 𝑦
  • B 9 1 6 > 𝑦
  • C 1 9 > 𝑦
  • D 9 1 6 < 𝑦
  • E 1 6 9 < 𝑦

Q4:

The solution set of the inequality βˆ’ 1 3 π‘₯ < βˆ’ 1 0 , where π‘₯ ∈ β„š + , is a subset of which of the following?

  • A βˆ…
  • B β„š βˆ’
  • C β„€ +
  • D β„š +
  • E β„€ βˆ’

Q5:

Write an inequality to describe the following, and then solve it: The quotient of a number and 9 is more than 2.

  • A 2 π‘₯ < 1 9 , π‘₯ < 1 1 8
  • B π‘₯ 9 < 2 , π‘₯ < 1 8
  • C 2 π‘₯ > 1 9 , π‘₯ > 1 1 8
  • D π‘₯ 9 > 2 , π‘₯ > 1 8
  • E π‘₯ 9 ≀ 2 , π‘₯ ≀ 1 8

Q6:

Find the solution set of βˆ’ 4 ≀ π‘₯ < 0 , where π‘₯ ∈ β„• .

  • A { βˆ’ 4 , βˆ’ 3 , βˆ’ 2 }
  • B { βˆ’ 3 , βˆ’ 2 , βˆ’ 1 , 0 }
  • C { βˆ’ 3 , βˆ’ 2 , βˆ’ 1 }
  • D βˆ…

Q7:

Solve the inequality 1 1 π‘₯ > 7 7 in β„š .

  • A { π‘₯ ∢ π‘₯ ∈ β„š , π‘₯ < 7 }
  • B { π‘₯ ∢ π‘₯ ∈ β„š , π‘₯ < βˆ’ 7 }
  • C { π‘₯ ∢ π‘₯ ∈ β„š , π‘₯ > 6 6 }
  • D { π‘₯ ∢ π‘₯ ∈ β„š , π‘₯ > 7 }

Q8:

Find the solution set of βˆ’ 3 π‘₯ β‰₯ 3 where π‘₯ ∈ β„• .

  • A { βˆ’ 1 }
  • B { βˆ’ 1 , 0 }
  • C { 0 , 1 , 2 , … }
  • D βˆ…

Q9:

Find the solution set of . Write your answer as an interval.

  • A
  • B
  • C
  • D
  • E

Q10:

Rewrite π‘₯ 6 < βˆ’ 2 so that only π‘₯ appears on the left-hand side.

  • A π‘₯ > βˆ’ 1 3
  • B π‘₯ > βˆ’ 1 2
  • C π‘₯ < βˆ’ 1 3
  • D π‘₯ < βˆ’ 1 2

Q11:

Given that π‘₯ ∈ β„• , determine the solution set of the inequality βˆ’ π‘₯ > βˆ’ 1 3 2 .

  • A π‘₯ > 1 3 2
  • B { βˆ’ 1 3 1 , βˆ’ 1 3 0 , βˆ’ 1 2 9 , … }
  • C { 1 3 2 }
  • D { 0 , 1 , 2 , … , 1 3 1 }

Q12:

Find the solution set of βˆ’ 4 π‘₯ > 8 given that π‘₯ ∈ β„• .

  • A { 2 }
  • B { 4 , 3 }
  • C { βˆ’ 3 , βˆ’ 2 }
  • D βˆ…

Q13:

Which of the following inequalities is equivalent to βˆ’ 4 π‘₯ > βˆ’ 2 ?

  • A π‘₯ = 1 2
  • B π‘₯ < 8
  • C π‘₯ > 1 2
  • D π‘₯ < 1 2
  • E π‘₯ β‰₯ 1 2

Q14:

Emma wants to send books to a friend. She has a prepaid parcel bag in which she can send items weighing up to 1 kg. Given that each book weighs 120 g, which of the following describes the condition on 𝑛 , the number of books that Emma can send in her prepaid parcel bag?

  • A 𝑛 Γ— 1 2 0 < 1 0 0 0
  • B 𝑛 Γ— 1 2 0 β‰₯ 1 0 0 0
  • C 𝑛 Γ— 1 2 0 > 1 0 0 0
  • D 𝑛 Γ— 1 2 0 ≀ 1 0 0 0
  • E 𝑛 Γ· 1 2 0 ≀ 1 0 0 0

Q15:

Solve the inequality 1 . 5 π‘₯ ≀ 5 for π‘₯ .

  • A π‘₯ ≀ 7 2
  • B π‘₯ ≀ 3 1 0
  • C π‘₯ ≀ 1 3 2
  • D π‘₯ ≀ 1 0 3
  • E π‘₯ β‰₯ 1 0 3

Q16:

Write an inequality to describe the following, and then solve it: Negative five times a number is at least βˆ’ 4 5 .

  • A βˆ’ 5 π‘₯ β‰₯ βˆ’ 4 5 , π‘₯ β‰₯ 9
  • B βˆ’ 5 π‘₯ ≀ βˆ’ 4 5 , π‘₯ β‰₯ 9
  • C βˆ’ 5 π‘₯ ≀ βˆ’ 4 5 , π‘₯ ≀ 9
  • D βˆ’ 5 π‘₯ β‰₯ βˆ’ 4 5 , π‘₯ ≀ 9
  • E βˆ’ 5 π‘₯ < βˆ’ 4 5 , π‘₯ > 9

Q17:

Which of the following inequalities is equivalent to βˆ’ 4 π‘₯ ≀ βˆ’ 1 ?

  • A π‘₯ = 1 4
  • B π‘₯ β‰₯ 4
  • C π‘₯ < 1 4
  • D π‘₯ β‰₯ 1 4
  • E π‘₯ ≀ 1 4