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Worksheet: Solving Inequalities by Multiplication

Q1:

Solve the inequality βˆ’ 7 1 0 π‘₯ ≀ βˆ’ 8 in β„š .

  • A  π‘₯ ∢ π‘₯ ∈ β„š , π‘₯ ≀ 8 0 7 
  • B  π‘₯ ∢ π‘₯ ∈ β„š , π‘₯ β‰₯ 2 8 5 
  • C  π‘₯ ∢ π‘₯ ∈ β„š , π‘₯ β‰₯ βˆ’ 8 0 7 
  • D  π‘₯ ∢ π‘₯ ∈ β„š , π‘₯ β‰₯ 8 0 7 
  • E  π‘₯ ∢ π‘₯ ∈ β„š , π‘₯ ≀ βˆ’ 8 0 7 

Q2:

Given that βˆ’ 1 ≀ βˆ’ 6 π‘₯ 1 0 βˆ’ 1 ≀ 5 , find the greatest possible value of π‘₯ + 8 .

Q3:

Fill in the blank in the following rule on inequalities: If π‘₯ > 𝑦 and 𝑧 > 0 , then π‘₯ 𝑧 𝑦 𝑧 .

  • A =
  • B <
  • C >

Q4:

Given that π‘₯ is a whole number and 9 2 5 < π‘₯ 2 5 < 1 4 2 5 , what are the possible values of π‘₯ ?

  • A 1 1 , 1 2 , 1 3 , 1 4
  • B 9 , 1 0 , 1 1 , 1 2
  • C 1 0 , 1 2 , 1 4 , 1 3
  • D 1 0 , 1 1 , 1 2 , 1 3

Q5:

If π‘₯ is a nonnegative integer, under what condition is the expression √ π‘₯ < √ 6 4 true?

  • A π‘₯ > 1 2 8
  • B π‘₯ > 6 4
  • C π‘₯ < 1 2 8
  • D π‘₯ < 6 4
  • E π‘₯ > 1 6

Q6:

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

  • A
  • B
  • C
  • D
  • E