Worksheet: One-step Inequalities: Multiplication or Division

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


Solve 5๐‘ฅ>45 for ๐‘ฅ.

  • A๐‘ฅ>40
  • B๐‘ฅ>9
  • C๐‘ฅ=9
  • D๐‘ฅ<9
  • E๐‘ฅ=40


Solve the following inequality: 14<49๐‘ฆ.

  • A19<๐‘ฆ
  • B19>๐‘ฆ
  • C169<๐‘ฆ
  • D916>๐‘ฆ
  • E916<๐‘ฆ


If โˆ’42๐‘ฅ<โˆ’41, then .

  • A๐‘ฅ>โˆ’4142
  • B๐‘ฅ>4142
  • C๐‘ฅ<4142
  • D๐‘ฅ<โˆ’4142


Solve the following inequality: โˆ’2โ‰ฅ๐‘ฅ0.8.

  • A๐‘ฅโ‰ฅโˆ’1.6
  • B๐‘ฅโ‰ฅโˆ’2.5
  • C๐‘ฅโ‰ฅโˆ’2.8
  • D๐‘ฅโ‰คโˆ’2.8
  • E๐‘ฅโ‰คโˆ’1.6


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

  • A2๐‘ฅ<19, ๐‘ฅ<118
  • B๐‘ฅ9>2, ๐‘ฅ>18
  • C๐‘ฅ9โ‰ค2, ๐‘ฅโ‰ค18
  • D2๐‘ฅ>19, ๐‘ฅ>118
  • E๐‘ฅ9<2, ๐‘ฅ<18


The solution set of the inequality โˆ’13๐‘ฅ<โˆ’10, where ๐‘ฅโˆˆโ„š๏Šฐ, is a subset of which of the following?

  • Aโˆ…
  • Bโ„š๏Šฐ
  • Cโ„ค๏Šฐ
  • Dโ„š๏Šฑ
  • Eโ„ค๏Šฑ


Solve the inequality 11๐‘ฅ>77 in โ„š.

  • A{๐‘ฅโˆถ๐‘ฅโˆˆโ„š,๐‘ฅ>7}
  • B{๐‘ฅโˆถ๐‘ฅโˆˆโ„š,๐‘ฅ<โˆ’7}
  • C{๐‘ฅโˆถ๐‘ฅโˆˆโ„š,๐‘ฅ>66}
  • D{๐‘ฅโˆถ๐‘ฅโˆˆโ„š,๐‘ฅ<7}


Solve the inequality โˆ’710๐‘ฅโ‰คโˆ’8 in โ„š.

  • A๏ฌ๐‘ฅโˆถ๐‘ฅโˆˆโ„š,๐‘ฅโ‰คโˆ’807๏ธ
  • B๏ฌ๐‘ฅโˆถ๐‘ฅโˆˆโ„š,๐‘ฅโ‰ฅ807๏ธ
  • C๏ฌ๐‘ฅโˆถ๐‘ฅโˆˆโ„š,๐‘ฅโ‰ค807๏ธ
  • D๏ฌ๐‘ฅโˆถ๐‘ฅโˆˆโ„š,๐‘ฅโ‰ฅโˆ’807๏ธ
  • E๏ฌ๐‘ฅโˆถ๐‘ฅโˆˆโ„š,๐‘ฅโ‰ฅ285๏ธ


Find the solution set of โˆ’3๐‘ฅโ‰ฅ3 where ๐‘ฅโˆˆโ„•.

  • A{โˆ’1}
  • Bโˆ…
  • C{0,1,2,โ€ฆ}
  • D{โˆ’1,0}


Fill in the blank in the following rule on inequalities: If ๐‘ฅ>๐‘ฆ and ๐‘ง>0, then ๐‘ฅ๐‘ง๐‘ฆ๐‘ง.

  • A=
  • B<
  • C>


Rewrite ๐‘ฅ6<โˆ’2 so that only ๐‘ฅ appears on the left-hand side.

  • A๐‘ฅ<โˆ’13
  • B๐‘ฅ<โˆ’12
  • C๐‘ฅ>โˆ’12
  • D๐‘ฅ>โˆ’13


Given that ๐‘ฅโˆˆโ„•, determine the solution set of the inequality โˆ’๐‘ฅ>โˆ’132.

  • A{132}
  • B{โˆ’131,โˆ’130,โˆ’129,โ€ฆ}
  • C๐‘ฅ>132
  • D{0,1,2,โ€ฆ,131}


Find the solution set of โˆ’4๐‘ฅ>8 given that ๐‘ฅโˆˆโ„•.

  • A{โˆ’3,โˆ’2}
  • Bโˆ…
  • C{4,3}
  • D{2}


Which of the following inequalities is equivalent to โˆ’4๐‘ฅ>โˆ’2?

  • A๐‘ฅ<8
  • B๐‘ฅโ‰ฅ12
  • C๐‘ฅ>12
  • D๐‘ฅ<12
  • E๐‘ฅ=12


Find the solution set of the inequality ๐‘ฅโˆš4โˆ’โˆš25โ‰คโˆš4+โˆš25 in โ„. Give your answer in interval notation.

  • A[โˆ’21,โˆž)
  • B[4,โˆž)
  • C[21,โˆž)
  • D(โˆ’21,โˆž)
  • E(โˆ’โˆž,โˆ’21]


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 ๐‘›, the number of books that Emma can send in her prepaid parcel bag?

  • A๐‘›ร—120โ‰ค1,000
  • B๐‘›ร—120>1,000
  • C๐‘›ร—120โ‰ฅ1,000
  • D๐‘›ร—120<1,000
  • E๐‘›รท120โ‰ค1,000


Solve the inequality 1.5๐‘ฅโ‰ค5 for ๐‘ฅ.

  • A๐‘ฅโ‰ค310
  • B๐‘ฅโ‰ค103
  • C๐‘ฅโ‰ค132
  • D๐‘ฅโ‰ฅ103
  • E๐‘ฅโ‰ค72


Select the option that is equivalent to ๐‘ฅโ‰ค3.

  • Aโˆ’๐‘ฅ<โˆ’3
  • Bโˆ’๐‘ฅโ‰คโˆ’3
  • Cโˆ’๐‘ฅ>โˆ’3
  • Dโˆ’๐‘ฅโ‰ฅโˆ’3


Write an inequality to describe the following, and then solve it: Negative five times a number is at least โˆ’45.

  • Aโˆ’5๐‘ฅ<โˆ’45, ๐‘ฅ>9
  • Bโˆ’5๐‘ฅโ‰คโˆ’45, ๐‘ฅโ‰ค9
  • Cโˆ’5๐‘ฅโ‰คโˆ’45, ๐‘ฅโ‰ฅ9
  • Dโˆ’5๐‘ฅโ‰ฅโˆ’45, ๐‘ฅโ‰ค9
  • Eโˆ’5๐‘ฅโ‰ฅโˆ’45, ๐‘ฅโ‰ฅ9


Which of the following inequalities is equivalent to โˆ’4๐‘ฅโ‰คโˆ’1?

  • A๐‘ฅ=14
  • B๐‘ฅ<14
  • C๐‘ฅโ‰ค14
  • D๐‘ฅโ‰ฅ4
  • E๐‘ฅโ‰ฅ14


Which of the following inequalities has a solution that involves reversing its sign?

  • A11๐‘ฅ>19
  • B9๐‘ฅ>โˆ’35
  • C13๐‘ฅ>25
  • Dโˆ’12๐‘ฅ>34
  • E14๐‘ฅ>16


Which of the following inequalities is equivalent to 5๐‘ฅ<โˆ’4?

  • A๐‘ฅ=โˆ’45
  • B๐‘ฅ<โˆ’45
  • C๐‘ฅโ‰คโˆ’45
  • D๐‘ฅ>โˆ’45
  • E๐‘ฅ<โˆ’20


Solve the following inequality: โˆ’10๐‘ฅโ‰ฅ60.

  • A๐‘ฅโ‰ค6
  • B๐‘ฅโ‰ฅ6
  • C๐‘ฅโ‰คโˆ’6
  • D๐‘ฅโ‰ฅโˆ’6


Which of the following inequalities is equivalent to 4๐‘ฅโ‰ฅ5?

  • A๐‘ฅโ‰ฅ54
  • B๐‘ฅ<54
  • C๐‘ฅโ‰ค54
  • D๐‘ฅโ‰ฅ20


A shipping company is loading boxes onto a truck. The truck can carry a maximum of 6,500 pounds of cargo. If each box weighs 100 pounds, write and solve an inequality that can be used to find the number of boxes loaded onto the truck.

  • A6,500๐‘ฅโ‰ฅ100, ๐‘ฅโ‰ฅ165
  • B100๐‘ฅ>6,500, ๐‘ฅ>65
  • C100๐‘ฅโ‰ฅ6,500, ๐‘ฅโ‰ฅ65
  • D6,500๐‘ฅโ‰ค100, ๐‘ฅโ‰ค165
  • E100๐‘ฅโ‰ค6,500, ๐‘ฅโ‰ค65

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