Worksheet: One-step Inequalities: Addition or Subtraction

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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+𝑎𝑚+𝑎.

  • A >
  • B <
  • C =

Q2:

If 𝑎+46≥39, 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+104104.

  • A <
  • B >
  • C =

Q4:

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

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 − 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

Q6:

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

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

Q7:

Given that 𝑥+34≥46, what number do you need to add to both sides of the inequality to solve for 𝑥?

Q8:

Solve the inequality 823>𝑎+435 in ℚ.

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

Q9:

Given that 213≥𝑥−514, what number do you need to add to both sides of the inequality to solve for 𝑥?

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

Q10:

Given that 𝑥−23≥−12, what number do you need to add to both sides of the inequality to solve for 𝑥?

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

Q11:

Solve the following inequality: 𝑑−12≤14.

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

Q12:

If 𝑎+23≥38, then .

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

Q13:

William limits his video gaming to no more than 11 hours a week. He has already played for 8 hours this week. Write an inequality to find out how much more time William can spend playing video games this week, and then solve it.

  • A 𝑥 − 1 1 ≥ 8 , 𝑥 ≥ 1 9
  • B 𝑥 + 8 ≤ 1 1 , 𝑥 ≤ 3
  • C 𝑥 − 8 ≥ 1 1 , 𝑥 ≥ 1 9
  • D 𝑥 + 8 ≥ 1 1 , 𝑥 ≥ 3
  • E 𝑥 − 8 ≤ 1 1 , 𝑥 ≤ 1 9

Q14:

Asuka hopes that someday she will manage to collect more than 85 vintage comic books. She currently has 63 comics. Write and solve an inequality that can be used to determine how many books Asuka needs to get to complete her collection.

  • A 𝑥 − 8 5 > 6 3 , 𝑥 > 1 4 8
  • B 𝑥 − 6 3 < 8 5 , 𝑥 < 1 4 8
  • C 𝑥 + 6 3 < 8 5 , 𝑥 < 2 2
  • D 𝑥 + 6 3 > 8 5 , 𝑥 > 2 2
  • E 𝑥 − 6 3 > 8 5 , 𝑥 > 2 2

Q15:

Write an inequality that represents the following problem, and then solve it: The sum of a number and 7.2 is at least 12.4.

  • A 𝑥 − 7 . 2 ≤ 1 2 . 4 , 𝑥 ≤ 1 9 . 6
  • B 𝑥 + 7 . 2 ≤ 1 2 . 4 , 𝑥 ≤ 5 . 2
  • C 𝑥 − 1 2 . 4 ≤ 7 . 2 , 𝑥 ≤ 1 9 . 6
  • D 𝑥 + 7 . 2 ≥ 1 2 . 4 , 𝑥 ≥ 5 . 2
  • E 𝑥 − 7 . 2 ≥ 1 2 . 4 , 𝑥 ≥ 1 9 . 6

Q16:

Daniel wants to buy groceries. He wants to have at least $80 cash with him, and he currently has $15. Write and solve an inequality that would determine how much cash Daniel should withdraw from the bank.

  • A 𝑥 + 1 5 ≥ 8 0 , 𝑥 ≥ 6 5
  • B 𝑥 + 1 5 ≤ 8 0 , 𝑥 ≤ 6 5
  • C 𝑥 − 1 5 ≥ 8 0 , 𝑥 ≥ 9 5
  • D 𝑥 − 8 0 ≤ 1 5 , 𝑥 ≤ 9 5
  • E 𝑥 + 1 5 ≥ 8 0 , 𝑥 ≥ 9 5

Q17:

Write the solution set of 𝑥−2<1 given that 𝑥∈ℕ.

  • A { − 1 , 0 , 1 , 2 }
  • B { 0 , 1 , 2 , 3 }
  • C { 0 , 1 , 2 }
  • D { 1 , 2 , 3 }

Q18:

Write the solution set of 𝑥−7≥−2 given that 𝑥∈ℕ.

  • A { − 1 , 0 , 1 , 2 , 3 , 4 }
  • B { 1 , 2 , 3 , 4 , 5 }
  • C { 6 , 7 , 8 , … }
  • D { 5 , 6 , 7 , … }

Q19:

Find the solution set of 𝑥+2<6 given that 𝑥∈ℤ.

  • A { 1 , 2 , 3 , 4 }
  • B { 0 , 1 , 2 , 3 , 4 }
  • C { − 1 , 0 , 1 , 2 , 3 }
  • D { 1 , 2 , 3 }

Q20:

Write an inequality to describe the following problem, and then solve it: The result of subtracting −4 from a number is less than 21.

  • A 𝑥 − ( − 2 1 ) < 4 , 𝑥 < 1 7
  • B 𝑥 − ( − 4 ) > 2 1 , 𝑥 > 1 7
  • C 𝑥 + ( − 4 ) < 2 1 , 𝑥 < 2 5
  • D 𝑥 + ( − 4 ) > 2 1 , 𝑥 > 2 5
  • E 𝑥 − ( − 4 ) < 2 1 , 𝑥 < 1 7

Q21:

Find the solution set of 𝑥+5<−6, given that 𝑥∈ℕ.

  • A { − 1 1 }
  • B { 1 1 }
  • C { − 1 1 , − 1 2 , − 1 3 , … }
  • D { − 1 0 , − 9 }
  • E ∅

Q22:

Find the solution set of 𝑥−8≤−5 given that 𝑥∈ℕ.

  • A { − 1 , 0 , 1 , 3 }
  • B { 1 , 2 , 3 }
  • C { 0 , 1 , 2 , 3 }
  • D { − 1 , 0 , 1 , 2 }

Q23:

Find the solution set of the inequality 𝑥−43>11, where 𝑥∈ℤ.

  • A { 5 5 , 5 6 , 5 7 , 5 8 , … }
  • B { − 3 2 , − 3 1 , − 3 0 , − 2 9 , … }
  • C { 5 4 , 5 5 , 5 6 , 5 7 , … }
  • D { 3 3 , 3 4 , 3 5 , 3 6 , … }
  • E { − 3 1 , − 3 0 , − 2 9 , − 2 8 , … }

Q24:

Find the solution set of 𝑥+19>−13 given that 𝑥∈ℕ.

  • A { 7 , 8 , … }
  • B ℕ
  • C { 3 2 , 3 3 , … }
  • D { 0 , 1 , … , 3 1 }

Q25:

Given that 𝑥∈ℤ, solve the inequality 𝑥+7<−7.

  • A { 𝑥 ∶ 𝑥 ∈ ℤ , 𝑥 < 0 }
  • B { 𝑥 ∶ 𝑥 ∈ ℤ , 𝑥 ≥ − 1 4 }
  • C { 𝑥 ∶ 𝑥 ∈ ℤ , 𝑥 ≤ − 1 4 }
  • D { 𝑥 ∶ 𝑥 ∈ ℤ , 𝑥 < − 1 4 }
  • E { 𝑥 ∶ 𝑥 ∈ ℤ , 𝑥 > − 1 4 }

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