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Worksheet: One-Step First-Degree Inequalities

Q1:

Write an inequality to describe the following problem, and then solve it: The result of subtracting βˆ’ 4 from a number is less than 21.

  • A π‘₯ βˆ’ ( βˆ’ 2 1 ) < 4 , π‘₯ < 1 7
  • B π‘₯ + ( βˆ’ 4 ) < 2 1 , π‘₯ < 2 5
  • C π‘₯ + ( βˆ’ 4 ) > 2 1 , π‘₯ > 2 5
  • D π‘₯ βˆ’ ( βˆ’ 4 ) < 2 1 , π‘₯ < 1 7
  • E π‘₯ βˆ’ ( βˆ’ 4 ) > 2 1 , π‘₯ > 1 7

Q2:

Write the solution set of π‘₯ βˆ’ 2 < 1 given that π‘₯ ∈ β„• .

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

Q3:

Write the solution set of π‘₯ + 1 < 6 given that π‘₯ ∈ β„• .

  • A { 1 , 2 , 3 , 4 , 5 }
  • B { βˆ’ 1 , 0 , 1 , 2 , 3 , 4 }
  • C { 0 , 1 , 2 , 3 , 4 , 5 }
  • D { 0 , 1 , 2 , 3 , 4 }

Q4:

Write the solution set of π‘₯ βˆ’ 7 β‰₯ βˆ’ 2 given that π‘₯ ∈ β„• .

  • A { 1 , 2 , 3 , 4 , 5 }
  • B { βˆ’ 1 , 0 , 1 , 2 , 3 , 4 }
  • C { 6 , 7 , 8 , … }
  • D { 5 , 6 , 7 , … }

Q5:

Write and solve an inequality to determine the side length of a regular hexagon with a perimeter of at least 12 feet.

  • A 6 π‘₯ ≀ 1 2 , π‘₯ ≀ 2
  • B 1 2 π‘₯ β‰₯ 6 , π‘₯ β‰₯ 1 2
  • C 1 2 π‘₯ ≀ 6 , π‘₯ ≀ 1 2
  • D 6 π‘₯ β‰₯ 1 2 , π‘₯ β‰₯ 2
  • E 1 2 π‘₯ β‰₯ 5 , π‘₯ β‰₯ 5 1 2

Q6:

Write and solve an inequality for the following problem: 16 more than a number is not more than 29.

  • A π‘₯ βˆ’ 1 6 ≀ 2 9 , π‘₯ ≀ 4 5
  • B π‘₯ + 1 6 β‰₯ 2 9 , π‘₯ β‰₯ 1 3
  • C π‘₯ βˆ’ 1 6 β‰₯ 2 9 , π‘₯ β‰₯ 4 5
  • D π‘₯ + 1 6 ≀ 2 9 , π‘₯ ≀ 1 3
  • E π‘₯ + 2 9 β‰₯ 1 6 , π‘₯ β‰₯ 1 3

Q7:

Determine the solution set of the inequality in .

  • A
  • B
  • C
  • D

Q8:

What is the solution set of in ?

  • A
  • B
  • C
  • D

Q9:

Find the solution set of π‘₯ + 5 < βˆ’ 6 , given that π‘₯ ∈ β„• .

  • A { βˆ’ 1 1 }
  • B { βˆ’ 1 0 , βˆ’ 9 }
  • C { βˆ’ 1 1 , βˆ’ 1 2 , βˆ’ 1 3 , … }
  • D βˆ…
  • E { 1 1 }

Q10:

Find the solution set of π‘₯ + 2 < 6 given that π‘₯ ∈ β„€ + .

  • A { 1 , 2 , 3 , 4 }
  • B { βˆ’ 1 , 0 , 1 , 2 , 3 }
  • C { 0 , 1 , 2 , 3 , 4 }
  • D { 1 , 2 , 3 }

Q11:

Find the solution set of π‘₯ βˆ’ 8 ≀ βˆ’ 5 given that π‘₯ ∈ β„• .

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

Q12:

Find the solution set of the inequality π‘₯ βˆ’ 4 3 > 1 1 , where π‘₯ ∈ β„€ .

  • A { βˆ’ 3 1 , βˆ’ 3 0 , βˆ’ 2 9 , βˆ’ 2 8 , … }
  • B { 5 4 , 5 5 , 5 6 , 5 7 , … }
  • C { βˆ’ 3 2 , βˆ’ 3 1 , βˆ’ 3 0 , βˆ’ 2 9 , … }
  • D { 5 5 , 5 6 , 5 7 , 5 8 , … }
  • E { 3 3 , 3 4 , 3 5 , 3 6 , … }

Q13:

Find the solution set of the inequality π‘₯ + 4 6 > βˆ’ 4 3 , where π‘₯ ∈ β„€ .

  • A { 4 , 5 , 6 , 7 , … }
  • B { βˆ’ 8 9 , βˆ’ 8 8 , βˆ’ 8 7 , βˆ’ 8 6 , … }
  • C { 3 , 4 , 5 , 6 , … }
  • D { βˆ’ 8 8 , βˆ’ 8 7 , βˆ’ 8 6 , βˆ’ 8 5 , … }
  • E { βˆ’ 2 , βˆ’ 1 , 0 , 1 , … }

Q14:

Find the solution set of π‘₯ + 1 9 > βˆ’ 1 3 given that π‘₯ ∈ β„• .

  • A { 7 , 8 , … }
  • B { 0 , 1 , … , 3 1 }
  • C { 3 2 , 3 3 , … }
  • D β„•

Q15:

Given that π‘₯ ∈ β„€ , solve the inequality π‘₯ + 7 < βˆ’ 7 .

  • A { π‘₯ ∢ π‘₯ ∈ β„€ , π‘₯ > βˆ’ 1 4 }
  • B { π‘₯ ∢ π‘₯ ∈ β„€ , π‘₯ ≀ βˆ’ 1 4 }
  • C { π‘₯ ∢ π‘₯ ∈ β„€ , π‘₯ β‰₯ βˆ’ 1 4 }
  • D { π‘₯ ∢ π‘₯ ∈ β„€ , π‘₯ < βˆ’ 1 4 }
  • E { π‘₯ ∢ π‘₯ ∈ β„€ , π‘₯ < 0 }

Q16:

Find the solution set of π‘₯ βˆ’ 9 < βˆ’ 7 , knowing that π‘₯ ∈ β„€ .

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

Q17:

Find the solution set of π‘₯ < 2 7 given that π‘₯ ∈ β„• .

  • A { 2 8 , 2 9 , … }
  • B βˆ…
  • C { 0 , 1 , … , 2 7 }
  • D { 0 , 1 , … , 2 6 }

Q18:

Find the solution set of the inequality π‘₯ 6 < 1 6 , where π‘₯ ∈ β„• .

  • A { 6 }
  • B { 1 }
  • C { 2 }
  • D { 0 }