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.

Q1:

Solve 5𝑥>45 for 𝑥.

  • A𝑥>40
  • B𝑥>9
  • C𝑥=9
  • D𝑥<9
  • E𝑥=40

Q2:

Solve the following inequality: 14<49𝑦.

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

Q3:

If 42𝑥<41, then .

  • A𝑥>4142
  • B𝑥>4142
  • C𝑥<4142
  • D𝑥<4142

Q4:

Solve the following inequality: 2𝑥0.8.

  • A𝑥1.6
  • B𝑥2.5
  • C𝑥2.8
  • D𝑥2.8
  • E𝑥1.6

Q5:

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

  • A2𝑥<19, 𝑥<118
  • B𝑥9>2, 𝑥>18
  • C𝑥92, 𝑥18
  • D2𝑥>19, 𝑥>118
  • E𝑥9<2, 𝑥<18

Q6:

The solution set of the inequality 13𝑥<10, where 𝑥, is a subset of which of the following?

  • A
  • B
  • C
  • D
  • E

Q7:

Solve the inequality 11𝑥>77 in .

  • A{𝑥𝑥,𝑥>7}
  • B{𝑥𝑥,𝑥<7}
  • C{𝑥𝑥,𝑥>66}
  • D{𝑥𝑥,𝑥<7}

Q8:

Solve the inequality 710𝑥8 in .

  • A𝑥𝑥,𝑥807
  • B𝑥𝑥,𝑥807
  • C𝑥𝑥,𝑥807
  • D𝑥𝑥,𝑥807
  • E𝑥𝑥,𝑥285

Q9:

Find the solution set of 3𝑥3 where 𝑥.

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

Q10:

Fill in the blank in the following rule on inequalities: If 𝑥>𝑦 and 𝑧>0, then 𝑥𝑧𝑦𝑧.

  • A=
  • B<
  • C>

Q11:

Rewrite 𝑥6<2 so that only 𝑥 appears on the left-hand side.

  • A𝑥<13
  • B𝑥<12
  • C𝑥>12
  • D𝑥>13

Q12:

Given that 𝑥, determine the solution set of the inequality 𝑥>132.

  • A{132}
  • B{131,130,129,}
  • C𝑥>132
  • D{0,1,2,,131}

Q13:

Find the solution set of 4𝑥>8 given that 𝑥.

  • A{3,2}
  • B
  • C{4,3}
  • D{2}

Q14:

Which of the following inequalities is equivalent to 4𝑥>2?

  • A𝑥<8
  • B𝑥12
  • C𝑥>12
  • D𝑥<12
  • E𝑥=12

Q15:

Find the solution set of the inequality 𝑥4254+25 in . Give your answer in interval notation.

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

Q16:

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×1201,000
  • B𝑛×120>1,000
  • C𝑛×1201,000
  • D𝑛×120<1,000
  • E𝑛÷1201,000

Q17:

Solve the inequality 1.5𝑥5 for 𝑥.

  • A𝑥310
  • B𝑥103
  • C𝑥132
  • D𝑥103
  • E𝑥72

Q18:

Select the option that is equivalent to 𝑥3.

  • A𝑥<3
  • B𝑥3
  • C𝑥>3
  • D𝑥3

Q19:

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

  • A5𝑥<45, 𝑥>9
  • B5𝑥45, 𝑥9
  • C5𝑥45, 𝑥9
  • D5𝑥45, 𝑥9
  • E5𝑥45, 𝑥9

Q20:

Which of the following inequalities is equivalent to 4𝑥1?

  • A𝑥=14
  • B𝑥<14
  • C𝑥14
  • D𝑥4
  • E𝑥14

Q21:

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

  • A11𝑥>19
  • B9𝑥>35
  • C13𝑥>25
  • D12𝑥>34
  • E14𝑥>16

Q22:

Which of the following inequalities is equivalent to 5𝑥<4?

  • A𝑥=45
  • B𝑥<45
  • C𝑥45
  • D𝑥>45
  • E𝑥<20

Q23:

Solve the following inequality: 10𝑥60.

  • A𝑥6
  • B𝑥6
  • C𝑥6
  • D𝑥6

Q24:

Which of the following inequalities is equivalent to 4𝑥5?

  • A𝑥54
  • B𝑥<54
  • C𝑥54
  • D𝑥20

Q25:

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.

  • A6,500𝑥100, 𝑥165
  • B100𝑥>6,500, 𝑥>65
  • C100𝑥6,500, 𝑥65
  • D6,500𝑥100, 𝑥165
  • E100𝑥6,500, 𝑥65

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.