Worksheet: One-step Inequalities: Addition or Subtraction

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+4639, then .

  • A𝑎85
  • B𝑎85
  • C𝑎7
  • D𝑎7
  • E𝑎7

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?

  • A𝑚=10+4
  • B𝑚104
  • C𝑚104
  • D𝑚>10+4
  • E𝑚10+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?

  • A𝑝5042
  • B𝑝<5042
  • C𝑝>5042
  • D𝑝<50+42
  • E𝑝5042

Q6:

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

  • A7𝑎
  • B7>𝑎
  • C𝑎>7
  • D𝑎7

Q7:

Given that 𝑥+3446, 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 .

  • A𝑎𝑎,𝑎<19915
  • B𝑎𝑎,𝑎<6115
  • C𝑎𝑎,𝑎<19915
  • D𝑎𝑎,𝑎>6115

Q9:

Given that 213𝑥514, what number do you need to add to both sides of the inequality to solve for 𝑥?

  • A214
  • B3512
  • C73
  • D214

Q10:

Given that 𝑥2312, what number do you need to add to both sides of the inequality to solve for 𝑥?

  • A23
  • B23
  • C12
  • D16

Q11:

Solve the following inequality: 𝑑1214.

  • A𝑑14
  • B𝑑34
  • C𝑑14
  • D𝑑>34
  • E𝑑34

Q12:

If 𝑎+2338, then .

  • A𝑎61
  • B𝑎61
  • C𝑎15
  • D𝑎15
  • E𝑎15

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.

  • A𝑥118, 𝑥19
  • B𝑥+811, 𝑥3
  • C𝑥811, 𝑥19
  • D𝑥+811, 𝑥3
  • E𝑥811, 𝑥19

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.

  • A𝑥85>63, 𝑥>148
  • B𝑥63<85, 𝑥<148
  • C𝑥+63<85, 𝑥<22
  • D𝑥+63>85, 𝑥>22
  • E𝑥63>85, 𝑥>22

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.

  • A𝑥7.212.4, 𝑥19.6
  • B𝑥+7.212.4, 𝑥5.2
  • C𝑥12.47.2, 𝑥19.6
  • D𝑥+7.212.4, 𝑥5.2
  • E𝑥7.212.4, 𝑥19.6

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.

  • A𝑥+1580, 𝑥65
  • B𝑥+1580, 𝑥65
  • C𝑥1580, 𝑥95
  • D𝑥8015, 𝑥95
  • E𝑥+1580, 𝑥95

Q17:

Write the solution set of 𝑥2<1 given that 𝑥.

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

Q18:

Write the solution set of 𝑥72 given that 𝑥.

  • 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.

  • 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.

  • A𝑥(21)<4, 𝑥<17
  • B𝑥(4)>21, 𝑥>17
  • C𝑥+(4)<21, 𝑥<25
  • D𝑥+(4)>21, 𝑥>25
  • E𝑥(4)<21, 𝑥<17

Q21:

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

  • A{11}
  • B{11}
  • C{11,12,13,}
  • D{10,9}
  • E

Q22:

Find the solution set of 𝑥85 given that 𝑥.

  • 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 𝑥43>11, where 𝑥.

  • A{55,56,57,58,}
  • B{32,31,30,29,}
  • C{54,55,56,57,}
  • D{33,34,35,36,}
  • E{31,30,29,28,}

Q24:

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

  • A{7,8,}
  • B
  • C{32,33,}
  • D{0,1,,31}

Q25:

Given that 𝑥, solve the inequality 𝑥+7<7.

  • A{𝑥𝑥,𝑥<0}
  • B{𝑥𝑥,𝑥14}
  • C{𝑥𝑥,𝑥14}
  • D{𝑥𝑥,𝑥<14}
  • E{𝑥𝑥,𝑥>14}

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