Worksheet: Two-Step Linear Inequalities

In this worksheet, we will practice solving a linear inequality in two steps.

Q1:

What can you say about 𝑥 > 2 7 − 6 ?

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

Q2:

Find the solution set of 3 𝑥 − 7 < − 4 given that 𝑥 ∈ ℕ .

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

Q3:

Determine the solution set of 2 − 𝑥 ≤ − 8 , where 𝑥 ∈ ℤ  .

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

Q4:

Find the solution set of − 5 𝑥 − 4 > 1 given that 𝑥 ∈ ℕ .

  • A { 1 }
  • B { − 3 , 2 }
  • C { 2 , 1 }
  • D ∅

Q5:

Mrs Dalia tells her maths class, “Five 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

Q6:

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 𝑥 can take.

  • A 4 𝑥 + 3 ≤ 2 𝑥 + 5
  • B 4 𝑥 + 2 > 3 𝑥 + 5
  • C 2 𝑥 − 4 < 5 𝑥 + 3
  • D 4 𝑥 + 2 < 3 𝑥 + 5
  • E 2 𝑥 − 4 > 5 𝑥 + 3

Solve your inequality.

  • A 𝑥 < 3
  • B 𝑥 > 4
  • C 𝑥 < 4
  • D 𝑥 > 3
  • E 𝑥 ≤ 5

Q7:

Given that 𝑥 ∈ ℚ , solve the inequality 7 𝑥 − 5 ≤ 8 .

  • A  𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≤ 8 7 
  • B  𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≤ 3 7 
  • C  𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 < 1 3 7 
  • D  𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≤ 1 3 7 
  • E  𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 < 3 7 

Q8:

Solve the inequality 1 9 + 7 𝑥 < 4 0 in ℚ .

  • A { 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 > 3 }
  • B { 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 > − 3 }
  • C  𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 < 5 9 7 
  • D { 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 < 3 }

Q9:

Find the solution set of the inequality 1 3 𝑥 + 1 < − 6 in ℝ . Give your answer in interval notation.

  • A [ − 2 1 , ∞ [
  • B ] − ∞ , − 2 1 ]
  • C ] − 2 1 , ∞ [
  • D ] − ∞ , − 2 1 [

Q10:

Find the solution set of the inequality 2 𝑥 − 2 > 4 in ℝ . Give your answer in interval notation.

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

Q11:

Find the solution set of the inequality 1 8 − 2 𝑥 ≤ − 1 8 in ℝ . Give your answer in interval notation.

  • A ( − ∞ , 1 8 )
  • B ( 1 8 , ∞ )
  • C ( − ∞ , − 1 8 ]
  • D [ 1 8 , ∞ )

Q12:

Solve 7 ≤ 2 𝑥 + 1 .

  • A 𝑥 ≤ − 3
  • B 𝑥 ≤ 3
  • C − 3 ≤ 𝑥
  • D 3 ≤ 𝑥

Q13:

Given that the solution set of the inequality 𝑎 ≤ 4 𝑥 − 3 ≤ 𝑏 is { 𝑥 ∶ 𝑥 ∈ ℚ , 3 ≤ 𝑥 ≤ 6 } , find the values of 𝑎 and 𝑏 .

  • A 𝑎 = 6 , 𝑏 = 9
  • B 𝑎 = 1 5 , 𝑏 = 2 7
  • C 𝑎 = 4 , 𝑏 = 7
  • D 𝑎 = 9 , 𝑏 = 2 1
  • E 𝑎 = 1 2 , 𝑏 = 2 4

Q14:

Find all values of 𝑥 that satisfy − 1 8 ≤ 𝑥 − 8 ≤ 1 2 . Write your answer as an interval.

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

Q15:

Solve 4 ≤ − 5 𝑥 − 1 .

  • A − 5 ≥ 𝑥
  • B 𝑥 ≥ − 1
  • C 𝑥 ≥ − 5
  • D − 1 ≥ 𝑥

Q16:

What can you say about 9 𝑥 − 2 = 1 0 ?

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

Q17:

What can you say about 6 𝑥 + 2 5 ?

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

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