Worksheet: Solving Inequalities by Adding or Subtracting

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In this worksheet, we will practice solving one-step linear inequalities by addition or subtraction.

Q1:

Fill in the blank in the following rule on inequalities: If 𝑦 > 𝑚 , then 𝑦 + 𝑎 𝑚 + 𝑎 .

  • A >
  • B <
  • C =

Q2:

If 𝑎 + 4 6 ≥ 3 9 , then .

  • A 𝑎 ≥ 8 5
  • B 𝑎 ≥ − 8 5
  • C 𝑎 ≥ − 7
  • D 𝑎 ≥ 7
  • E 𝑎 ≤ − 7

Q3:

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

  • A =
  • B <
  • C >

Q4:

Complete using ≤ , < , > , or ≥ : If 𝑏 ≤ − 5 , then 𝑏 + 1 − 4 .

  • A ≤
  • B <
  • C ≥
  • D >

Q5:

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

  • A 𝑚 ≤ 1 0 − 4
  • B 𝑚 = 1 0 + 4
  • C 𝑚 > 1 0 + 4
  • D 𝑚 ≥ 1 0 − 4
  • E 𝑚 ≥ 1 0 + 4

Q6:

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 − 4 2
  • B 𝑝 ≤ 5 0 − 4 2
  • C 𝑝 < 5 0 − 4 2
  • D 𝑝 < 5 0 + 4 2
  • E 𝑝 > 5 0 − 4 2

Q7:

Select the option that is equivalent to 𝑎 + 7 < 0 .

  • A − 7 > 𝑎
  • B − 7 ≥ 𝑎
  • C 𝑎 > − 7
  • D 𝑎 ≥ − 7

Q8:

Given that 𝑥 + 3 4 ≥ 4 6 , what number do you need to add to both sides of the inequality to solve for 𝑥 ?

Q9:

Solve the inequality 8 2 3 > 𝑎 + 4 3 5 in ℚ .

  • A 𝑎 ∶ 𝑎 ∈ ℚ , 𝑎 < 1 9 9 1 5
  • B 𝑎 ∶ 𝑎 ∈ ℚ , 𝑎 < − 1 9 9 1 5
  • C 𝑎 ∶ 𝑎 ∈ ℚ , 𝑎 > 6 1 1 5
  • D 𝑎 ∶ 𝑎 ∈ ℚ , 𝑎 < 6 1 1 5

Q10:

Given that 2 1 3 ≥ 𝑥 − 5 1 4 , what number do you need to add to both sides of the inequality to solve for 𝑥 ?

  • A − 7 3
  • B 2 1 4
  • C − 3 5 1 2
  • D − 2 1 4

Q11:

Given that 𝑥 − 2 3 ≥ − 1 2 , what number do you need to add to both sides of the inequality to solve for 𝑥 ?

  • A 2 3
  • B 1 6
  • C − 2 3
  • D 1 2

Q12:

Solve the following inequality: 𝑑 − 1 2 ≤ 1 4 .

  • A 𝑑 ≥ 1 4
  • B 𝑑 ≤ 3 4
  • C 𝑑 ≥ 3 4
  • D 𝑑 > 3 4
  • E 𝑑 ≤ 1 4

Q13:

If 𝑎 + 2 3 ≥ 3 8 , then .

  • A 𝑎 ≥ 1 5
  • B 𝑎 ≤ 1 5
  • C 𝑎 ≥ − 6 1
  • D 𝑎 ≥ 6 1
  • E 𝑎 ≥ − 1 5

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