Lesson Worksheet: One-step Inequalities: Multiplication or Division Mathematics • 6th Grade

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


Solve 5π‘₯>45 for π‘₯.

  • Aπ‘₯>40
  • Bπ‘₯>9
  • Cπ‘₯=9
  • Dπ‘₯<9
  • Eπ‘₯=40


Solve the following inequality: 14<49𝑦.

  • A19<𝑦
  • B19>𝑦
  • C169<𝑦
  • D916>𝑦
  • E916<𝑦


If βˆ’42π‘₯<βˆ’41, then .

  • Aπ‘₯>βˆ’4142
  • Bπ‘₯>4142
  • Cπ‘₯<4142
  • Dπ‘₯<βˆ’4142


Solve the following inequality: βˆ’2β‰₯π‘₯0.8.

  • Aπ‘₯β‰₯βˆ’1.6
  • Bπ‘₯β‰₯βˆ’2.5
  • Cπ‘₯β‰₯βˆ’2.8
  • Dπ‘₯β‰€βˆ’2.8
  • Eπ‘₯β‰€βˆ’1.6


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

  • A2π‘₯<19, π‘₯<118
  • Bπ‘₯9>2, π‘₯>18
  • Cπ‘₯9≀2, π‘₯≀18
  • D2π‘₯>19, π‘₯>118
  • Eπ‘₯9<2, π‘₯<18


The solution set of the inequality βˆ’13π‘₯<βˆ’10, where π‘₯βˆˆβ„šοŠ°, is a subset of which of the following?

  • Aβˆ…
  • Bβ„šοŠ°
  • Cβ„€οŠ°
  • Dβ„šοŠ±
  • Eβ„€οŠ±


Solve the inequality 11π‘₯>77 in β„š.

  • A{π‘₯∢π‘₯βˆˆβ„š,π‘₯>7}
  • B{π‘₯∢π‘₯βˆˆβ„š,π‘₯<βˆ’7}
  • C{π‘₯∢π‘₯βˆˆβ„š,π‘₯>66}
  • D{π‘₯∢π‘₯βˆˆβ„š,π‘₯<7}


Solve the inequality βˆ’710π‘₯β‰€βˆ’8 in β„š.

  • Aπ‘₯∢π‘₯βˆˆβ„š,π‘₯β‰€βˆ’807
  • Bπ‘₯∢π‘₯βˆˆβ„š,π‘₯β‰₯807
  • Cπ‘₯∢π‘₯βˆˆβ„š,π‘₯≀807
  • Dπ‘₯∢π‘₯βˆˆβ„š,π‘₯β‰₯βˆ’807
  • Eπ‘₯∢π‘₯βˆˆβ„š,π‘₯β‰₯285


Find the solution set of βˆ’3π‘₯β‰₯3 where π‘₯βˆˆβ„•.

  • A{βˆ’1}
  • Bβˆ…
  • C{0,1,2,…}
  • D{βˆ’1,0}


Fill in the blank in the following rule on inequalities: If π‘₯>𝑦 and 𝑧>0, then π‘₯𝑧𝑦𝑧.

  • A=
  • B<
  • C>


Rewrite π‘₯6<βˆ’2 so that only π‘₯ appears on the left-hand side.

  • Aπ‘₯<βˆ’13
  • Bπ‘₯<βˆ’12
  • Cπ‘₯>βˆ’12
  • Dπ‘₯>βˆ’13


Given that π‘₯βˆˆβ„•, determine the solution set of the inequality βˆ’π‘₯>βˆ’132.

  • A{132}
  • B{βˆ’131,βˆ’130,βˆ’129,…}
  • Cπ‘₯>132
  • D{0,1,2,…,131}


Find the solution set of βˆ’4π‘₯>8 given that π‘₯βˆˆβ„•.

  • A{βˆ’3,βˆ’2}
  • Bβˆ…
  • C{4,3}
  • D{2}


Which of the following inequalities is equivalent to βˆ’4π‘₯>βˆ’2?

  • Aπ‘₯<8
  • Bπ‘₯β‰₯12
  • Cπ‘₯>12
  • Dπ‘₯<12
  • Eπ‘₯=12


Find the solution set of the inequality π‘₯√4βˆ’βˆš25β‰€βˆš4+√25 in ℝ. Give your answer in interval notation.

  • A[βˆ’21,∞)
  • B[4,∞)
  • C[21,∞)
  • D(βˆ’21,∞)
  • E(βˆ’βˆž,βˆ’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 𝑛, the number of books that Emma can send in her prepaid parcel bag?

  • A𝑛×120≀1,000
  • B𝑛×120>1,000
  • C𝑛×120β‰₯1,000
  • D𝑛×120<1,000
  • E𝑛÷120≀1,000


Solve the inequality 1.5π‘₯≀5 for π‘₯.

  • Aπ‘₯≀310
  • Bπ‘₯≀103
  • Cπ‘₯≀132
  • Dπ‘₯β‰₯103
  • Eπ‘₯≀72


Select the option that is equivalent to π‘₯≀3.

  • Aβˆ’π‘₯<βˆ’3
  • Bβˆ’π‘₯β‰€βˆ’3
  • Cβˆ’π‘₯>βˆ’3
  • Dβˆ’π‘₯β‰₯βˆ’3


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

  • Aβˆ’5π‘₯<βˆ’45, π‘₯>9
  • Bβˆ’5π‘₯β‰€βˆ’45, π‘₯≀9
  • Cβˆ’5π‘₯β‰€βˆ’45, π‘₯β‰₯9
  • Dβˆ’5π‘₯β‰₯βˆ’45, π‘₯≀9
  • Eβˆ’5π‘₯β‰₯βˆ’45, π‘₯β‰₯9


Which of the following inequalities is equivalent to βˆ’4π‘₯β‰€βˆ’1?

  • Aπ‘₯=14
  • Bπ‘₯<14
  • Cπ‘₯≀14
  • Dπ‘₯β‰₯4
  • Eπ‘₯β‰₯14


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

  • A11π‘₯>19
  • B9π‘₯>βˆ’35
  • C13π‘₯>25
  • Dβˆ’12π‘₯>34
  • E14π‘₯>16


Which of the following inequalities is equivalent to 5π‘₯<βˆ’4?

  • Aπ‘₯=βˆ’45
  • Bπ‘₯<βˆ’45
  • Cπ‘₯β‰€βˆ’45
  • Dπ‘₯>βˆ’45
  • Eπ‘₯<βˆ’20


Solve the following inequality: βˆ’10π‘₯β‰₯60.

  • Aπ‘₯≀6
  • Bπ‘₯β‰₯6
  • Cπ‘₯β‰€βˆ’6
  • Dπ‘₯β‰₯βˆ’6


Which of the following inequalities is equivalent to 4π‘₯β‰₯5?

  • Aπ‘₯β‰₯54
  • Bπ‘₯<54
  • Cπ‘₯≀54
  • Dπ‘₯β‰₯20


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.

  • A6,500π‘₯β‰₯100, π‘₯β‰₯165
  • B100π‘₯>6,500, π‘₯>65
  • C100π‘₯β‰₯6,500, π‘₯β‰₯65
  • D6,500π‘₯≀100, π‘₯≀165
  • E100π‘₯≀6,500, π‘₯≀65

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