Chapter 1.2 Practice

Questions

Question 1

  1. Represent these sets as union of intervals
    1. \((2,4]\cup(3,5)\)
    2. \((-\infty,2]\cup(1,5]\)
    3. \([-5,6)\cup[6,5]\)
    4. \([-1,1]\cup \left((0,1)\cup(\frac{1}{2},2)\right)\)
    5. \([-1,1]\cap \left(-\infty,\frac{1}{2}\right)\)
    6. \([-1,1]\cap \left(\frac{1}{2},\infty\right)\)
    7. \([-4,\infty]\cap \left(-\infty,-5\right)\)
    8. \([-1,3]\cup \biggr((-\infty,5)\cap (2,\infty)\biggr)\)

Question 2

  1. Write out the solution set to the following inequalities as a union of intervals:
    1. \(x+1<4\)
    2. \(-x+1\leq 2\)
    3. \(2x+4\geq 3x+1\)
    4. \(x+4\geq 1\) or \(x-3<-11\)
    5. \(x+4\geq 1\) and \(x-3<-11\)
    6. \(3x+4\leq 10\) and \(2x-6>18\)
    7. \(2x+2\leq x\) and \(-2x-2>13\)

Answers

Question 1

    1. \((2,5)\)
    2. \((-\infty,5]\)
    3. \([-5,5]\)
    4. \([-1,2)\)
    5. \(\left[-1,\frac{1}{2}\right)\)
    6. \(\left(\frac{1}{2},1\right]\)
    7. \(\{\}\)
    8. \([-1,5)\)

Question 2

    1. \((-\infty,3)\)
    2. \([-1,\infty)\)
    3. \((-\infty,3)\)
    4. \((-\infty,-8)\cup[-3,\infty)\)
    5. \(\{\}\)
    6. \((-\infty,2]\cup (12,\infty)\)
    7. \(\left(-\infty,-\frac{15}{2}\right)\)

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