Answer to Question #299070 in Algebra for Molly

Question

b. Show on the real line and indicate in symbols each of the following:

S₁= {x: -7 < x < ∞ } ∩ {x: -∞ < x < 3}

S₂= (x:x ≥ ∞ } ∩ (x: x+ 3 < 6}

S3 = y: y²-2 y-3 < 0} U {y: -2 ≤ y ≤ 1}

Answer 1

$S_1$

$$-7<x<3$$

$S_2= \{x:x ≥ 0 \} ∩ \{x: x+ 3 < 6\}$

$S_2$

$$0\le x<3$$

$$y^2-2y-3<0$$

$$(y+1)(y-3)<0$$

$$-1<y<3$$

$S_3$

$$-2\le y<3$$