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Homework Help

Lesson: Two-Step Linear Inequalities

In this lesson, we will learn how to solve a linear inequality in two steps.

Sample Question Videos

00:51

Worksheet • 17 Questions • 1 Video

Q1:

What can you say about 9 π‘₯ βˆ’ 2 = 1 0 ?

  • A It is neither an equation nor an inequality.
  • B It is an equation.
  • C It is an inequality.

Q2:

What can you say about π‘₯ > 2 7 βˆ’ 6 ?

  • A It is an equation.
  • B It is an inequality.
  • C It is neither an equation nor an inequality.

Q3:

What can you say about 6 π‘₯ + 2 5 ?

  • A It is an inequality.
  • B It is neither an equation nor an inequality.
  • C It is an equation.

Q4:

Given that π‘₯ ∈ β„š , solve the inequality 7 π‘₯ βˆ’ 5 ≀ 8 .

  • A  π‘₯ ∢ π‘₯ ∈ β„š , π‘₯ ≀ 1 3 7 
  • B  π‘₯ ∢ π‘₯ ∈ β„š , π‘₯ < 3 7 
  • C  π‘₯ ∢ π‘₯ ∈ β„š , π‘₯ ≀ 3 7 
  • D  π‘₯ ∢ π‘₯ ∈ β„š , π‘₯ < 1 3 7 
  • E  π‘₯ ∢ π‘₯ ∈ β„š , π‘₯ ≀ 8 7 

Q5:

Find the solution set of 3 π‘₯ βˆ’ 7 < βˆ’ 4 given that π‘₯ ∈ β„• .

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

Q6:

Find the solution set of the inequality 1 3 π‘₯ + 1 < βˆ’ 6 in ℝ . Give your answer in interval notation.

  • A ] βˆ’ ∞ , βˆ’ 2 1 [
  • B ] βˆ’ ∞ , βˆ’ 2 1 ]
  • C ] βˆ’ 2 1 , ∞ [
  • D [ βˆ’ 2 1 , ∞ [

Q7:

Given that the solution set of the inequality π‘Ž ≀ 4 π‘₯ βˆ’ 3 ≀ 𝑏 is { π‘₯ ∢ π‘₯ ∈ β„š , 3 ≀ π‘₯ ≀ 6 } , find the values of π‘Ž and 𝑏 .

  • A π‘Ž = 9 , 𝑏 = 2 1
  • B π‘Ž = 1 2 , 𝑏 = 2 4
  • C π‘Ž = 1 5 , 𝑏 = 2 7
  • D π‘Ž = 4 , 𝑏 = 7
  • E π‘Ž = 6 , 𝑏 = 9

Q8:

Find the solution set of βˆ’ 5 π‘₯ βˆ’ 4 > 1 given that π‘₯ ∈ β„• .

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

Q9:

Solve the inequality 1 9 + 7 π‘₯ < 4 0 in β„š .

  • A { π‘₯ ∢ π‘₯ ∈ β„š , π‘₯ < 3 }
  • B { π‘₯ ∢ π‘₯ ∈ β„š , π‘₯ > βˆ’ 3 }
  • C  π‘₯ ∢ π‘₯ ∈ β„š , π‘₯ < 5 9 7 
  • D { π‘₯ ∢ π‘₯ ∈ β„š , π‘₯ > 3 }

Q10:

Find the solution set of the inequality 2 π‘₯ βˆ’ 2 > 4 in ℝ . Give your answer in interval notation.

  • A ] 3 , ∞ [
  • B ] 1 , ∞ [
  • C [ 3 , ∞ ]
  • D [ 3 , ∞ [
  • E ] 3 , ∞ ]

Q11:

Determine the solution set of 2 βˆ’ π‘₯ ≀ βˆ’ 8 , where π‘₯ ∈ β„€ + .

  • A { 1 0 , 1 1 , 1 2 , … }
  • B { 1 1 , 1 2 , 1 3 , … }
  • C βˆ…
  • D { 9 , 8 , 7 , … }

Q12:

Find all values of π‘₯ that satisfy βˆ’ 1 8 ≀ π‘₯ βˆ’ 8 ≀ 1 2 . Write your answer as an interval.

  • A [ βˆ’ 1 0 , 2 0 ]
  • B { βˆ’ 1 0 , 2 0 }
  • C ] βˆ’ 1 0 , 2 0 ]
  • D ] βˆ’ 2 6 , 4 ]
  • E [ βˆ’ 2 6 , 4 ]

Q13:

In the figure, the perimeter of the rectangle is less than that of the triangle.

Write an inequality that can be used to find the range of values that π‘₯ can take.

  • A 4 π‘₯ + 2 < 3 π‘₯ + 5
  • B 2 π‘₯ βˆ’ 4 > 5 π‘₯ + 3
  • C 4 π‘₯ + 2 > 3 π‘₯ + 5
  • D 2 π‘₯ βˆ’ 4 < 5 π‘₯ + 3
  • E 4 π‘₯ + 3 ≀ 2 π‘₯ + 5

Solve your inequality.

  • A π‘₯ < 3
  • B π‘₯ ≀ 5
  • C π‘₯ > 3
  • D π‘₯ > 4
  • E π‘₯ < 4

Q14:

Find the solution set of the inequality 1 8 βˆ’ 2 π‘₯ ≀ βˆ’ 1 8 in ℝ . Give your answer in interval notation.

  • A [ 1 8 , ∞ [
  • B ] 1 8 , ∞ [
  • C ] βˆ’ ∞ , βˆ’ 1 8 ]
  • D ] βˆ’ ∞ , 1 8 [

Q15:

Solve 7 ≀ 2 π‘₯ + 1 .

  • A 3 ≀ π‘₯
  • B π‘₯ ≀ 3
  • C βˆ’ 3 ≀ π‘₯
  • D π‘₯ ≀ βˆ’ 3

Q16:

Solve 4 ≀ βˆ’ 5 π‘₯ βˆ’ 1 .

  • A βˆ’ 1 β‰₯ π‘₯
  • B π‘₯ β‰₯ βˆ’ 1
  • C π‘₯ β‰₯ βˆ’ 5
  • D βˆ’ 5 β‰₯ π‘₯

Q17:

Mrs Dalia tells her maths class, β€œFive more than four times a number is more than 12.” Let represent the number, and write an inequality that represents her statement.

  • A
  • B
  • C
  • D
  • E
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