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: −2≥𝑥0.8.

  • A𝑥≥−1.6
  • B𝑥≥−2.5
  • C𝑥≥−2.8
  • D𝑥≤−2.8
  • E𝑥≤−1.6

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
  • C𝑥9≤2, 𝑥≤18
  • D2𝑥>19, 𝑥>118
  • E𝑥9<2, 𝑥<18

Q6:

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

  • A∅
  • Bℚ
  • Cℤ
  • Dℚ
  • Eℤ

Q7:

Solve the inequality 11𝑥>77 in ℚ.

  • A{𝑥∶𝑥∈ℚ,𝑥>7}
  • B{𝑥∶𝑥∈ℚ,𝑥<−7}
  • C{𝑥∶𝑥∈ℚ,𝑥>66}
  • D{𝑥∶𝑥∈ℚ,𝑥<7}

Q8:

Solve the inequality −710𝑥≤−8 in ℚ.

  • A𝑥∶𝑥∈ℚ,𝑥≤−807
  • B𝑥∶𝑥∈ℚ,𝑥≥807
  • C𝑥∶𝑥∈ℚ,𝑥≤807
  • D𝑥∶𝑥∈ℚ,𝑥≥−807
  • E𝑥∶𝑥∈ℚ,𝑥≥285

Q9:

Find the solution set of −3𝑥≥3 where 𝑥∈ℕ.

  • 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∈ℕ, 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∈ℕ.

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

Q14:

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

  • A𝑥<8
  • B𝑥≥12
  • C𝑥>12
  • D𝑥<12
  • E𝑥=12

Q15:

Find the solution set of the inequality 𝑥√4−√25≤√4+√25 in ℝ. 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×120≤1,000
  • B𝑛×120>1,000
  • C𝑛×120≥1,000
  • D𝑛×120<1,000
  • E𝑛÷120≤1,000

Q17:

Solve the inequality 1.5𝑥≤5 for 𝑥.

  • A𝑥≤310
  • B𝑥≤103
  • C𝑥≤132
  • D𝑥≥103
  • E𝑥≤72

Q18:

Select the option that is equivalent to 𝑥≤3.

  • A−𝑥<−3
  • B−𝑥≤−3
  • C−𝑥>−3
  • D−𝑥≥−3

Q19:

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

  • A−5𝑥<−45, 𝑥>9
  • B−5𝑥≤−45, 𝑥≤9
  • C−5𝑥≤−45, 𝑥≥9
  • D−5𝑥≥−45, 𝑥≤9
  • E−5𝑥≥−45, 𝑥≥9

Q20:

Which of the following inequalities is equivalent to −4𝑥≤−1?

  • A𝑥=14
  • B𝑥<14
  • C𝑥≤14
  • D𝑥≥4
  • E𝑥≥14

Q21:

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

  • A11𝑥>19
  • B9𝑥>−35
  • C13𝑥>25
  • D−12𝑥>34
  • E14𝑥>16

Q22:

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

  • A𝑥=−45
  • B𝑥<−45
  • C𝑥≤−45
  • D𝑥>−45
  • E𝑥<−20

Q23:

Solve the following inequality: −10𝑥≥60.

  • A𝑥≤6
  • B𝑥≥6
  • C𝑥≤−6
  • D𝑥≥−6

Q24:

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

  • A𝑥≥54
  • B𝑥<54
  • C𝑥≤54
  • D𝑥≥20

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.

  • A6,500𝑥≥100, 𝑥≥165
  • B100𝑥>6,500, 𝑥>65
  • C100𝑥≥6,500, 𝑥≥65
  • D6,500𝑥≤100, 𝑥≤165
  • E100𝑥≤6,500, 𝑥≤65

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