(Solved): Exercise 1.1. Give examples of numbers that are a) natural numbers b) integers c) integers but not ...

Exercise 1.1. Give examples of numbers that are a) natural numbers b) integers c) integers but not natural numbers d) rational numbers e) real numbers f) rational numbers but not integers Exercise 1.2. Which of the following numbers are natural numbers, integers, rational numbers, or real numbers? Which of these numbers are irrational? a) \( \frac{7}{3} \) b) \( -5 \) c) 0 d) 17,000 e) \( \frac{12}{4} \) f) \( \sqrt{7} \) g) \( \sqrt{25} \) Exercise 1.3. Evaluate the following absolute value expressions: a) \( |-8| \). b) \( |10| \). c) \( |-99| \), d) \( -|3| \), e) \( -|-2| \). i) \( -\sqrt{6} \) g) \( |3+4| \) h) \( |2-9| \), i) \( |-5.4| \), j) \( \left|-\frac{2}{3}\right| \), k) \( \left|\frac{5}{-2}\right| \). l) \( -\left|-\frac{-6}{-3}\right| \). Exercise 1.4. Solve for \( x \) : a) \( |x|=8 \) b) \( |x|=0 \) c) \( |x|=-3 \) d) \( |x+3|=10 \) e) \( |2 x+5|=9 \) f) \( |2-5 x|=22 \) g) \( |4 x|=-8 \) h) \( |-7 x-3|=0 \) i) \( |4-4 x|=44 \) j) \( -2 \cdot|2-3 x|=-12 \) k) \( 5+|2 x+7|=14 \) 1) \( -|-8-2 x|=-12 \) Exercise 1.6. Complete the table. Exercise 1.7. Solve for \( x \) and write the solution in interval notation. a) \( |x-4| \leq 7 \) b) \( |x-4| \geq 7 \) c) \( |x-4|>7 \) d) \( |2 x+7| \leq 13 \) e) \( |-2-4 x|>8 \) f) \( |4 x+2|<17 \) g) \( |15-3 x| \geq 6 \) h) \( \left|5 x-\frac{4}{3}\right|>\frac{2}{3} \) i) \( |\sqrt{2} x-\sqrt{2}| \leq \sqrt{8} \) j) \( |2 x+3|<-5 \) k) \( |5+5 x| \geq-2 \) l) \( |5+5 x|>0 \)