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Worksheet: Simplifying Inequalities by Adding or Subtracting

Q1:

Fill in the blank in the following rule on inequalities: If 𝑦 > π‘š , then 𝑦 + π‘Ž π‘š + π‘Ž .

  • A =
  • B <
  • C >

Q2:

If π‘Ž + 4 6 β‰₯ 3 9 , then .

  • A π‘Ž β‰₯ 8 5
  • B π‘Ž ≀ βˆ’ 7
  • C π‘Ž β‰₯ βˆ’ 8 5
  • D π‘Ž β‰₯ βˆ’ 7
  • E π‘Ž β‰₯ 7

Q3:

If π‘Ž + 4 5 β‰₯ βˆ’ 3 8 , then .

  • A π‘Ž β‰₯ 7
  • B π‘Ž ≀ βˆ’ 8 3
  • C π‘Ž β‰₯ βˆ’ 7
  • D π‘Ž β‰₯ βˆ’ 8 3
  • E π‘Ž β‰₯ 8 3

Q4:

Isabella has π‘š dollars. She wants to buy a book for $10 and a pencil case for $4. Which of the following describes the condition on π‘š for her to be able to afford both items?

  • A π‘š = 1 0 + 4
  • B π‘š > 1 0 + 4
  • C π‘š β‰₯ 1 0 βˆ’ 4
  • D π‘š β‰₯ 1 0 + 4
  • E π‘š ≀ 1 0 βˆ’ 4

Q5:

An online retailer offers free delivery when your purchase totals $50 or more. James is preparing his order. He has already chosen items which total $42. Which of the following describes the condition on 𝑝 , the cost of the additional items he needs to order for him to benefit from free delivery?

  • A 𝑝 ≀ 5 0 βˆ’ 4 2
  • B 𝑝 > 5 0 βˆ’ 4 2
  • C 𝑝 < 5 0 βˆ’ 4 2
  • D 𝑝 β‰₯ 5 0 βˆ’ 4 2
  • E 𝑝 < 5 0 + 4 2

Q6:

Given that , what number do you need to add to both sides of the inequality to solve for ?

  • A
  • B
  • C
  • D

Q7:

Solve the following inequality: 𝑑 βˆ’ 1 2 ≀ 1 4 .

  • A 𝑑 β‰₯ 3 4
  • B 𝑑 β‰₯ 1 4
  • C 𝑑 ≀ 1 4
  • D 𝑑 ≀ 3 4
  • E 𝑑 > 3 4

Q8:

Given that π‘₯ βˆ’ 2 3 β‰₯ βˆ’ 1 2 , what number do you need to add to both sides of the inequality to solve for π‘₯ ?

  • A 1 6
  • B βˆ’ 2 3
  • C 1 2
  • D 2 3

Q9:

Fill in the blank: If 𝑏 < 0 then 𝑏 + 1 0 4 1 0 4 .

  • A =
  • B >
  • C <

Q10:

Solve the inequality 5 4 9 > π‘Ž + 9 4 7 in β„š .

  • A  π‘Ž ∢ π‘Ž ∈ β„š , π‘Ž < 9 4 6 6 3 
  • B  π‘Ž ∢ π‘Ž ∈ β„š , π‘Ž < βˆ’ 9 4 6 6 3 
  • C  π‘Ž ∢ π‘Ž ∈ β„š , π‘Ž > βˆ’ 2 6 0 6 3 
  • D  π‘Ž ∢ π‘Ž ∈ β„š , π‘Ž < βˆ’ 2 6 0 6 3 

Q11:

Given that π‘₯ + 3 4 β‰₯ 4 6 , what number do you need to add to both sides of the inequality to solve for π‘₯ ?

Q12:

Given that π‘₯ βˆ’ 4 3 > 2 8 , what number do you need to add to both sides of the inequality to solve for π‘₯ ?

Q13:

Complete using ≀ , < , > , or β‰₯ : If 𝑏 ≀ βˆ’ 5 , then 𝑏 + 1 βˆ’ 4 .

  • A <
  • B >
  • C β‰₯
  • D ≀