Solving inequalities question?

Question

x^2-49<0,xer you get two solutions x<7 and x>-7 and you can put them together as {x|-7<x<7,xer} but how come for x^2>=25,xer you get x>=5 and x<=-5 but you cannot put them together

Answer 1

YOU can plot this on number line &amp; you will get the answer.

Answer 2

Because in x^2≥25, x belongs to two intervals, (-inf,-5] U [5, inf).

Answer 3

the first inequality is a conjunction. conjunction means you can join the two answers together. you can tell it is a conjunction when x is on the left side and it&#039;s less than what&#039;s on the right side. you can also make the less than sign look like a C.

&lt; is C for conjunction

the second one is a disjunction. meaning they are separate from each other. you can tell it&#039;s a disjunction if x is on the left side and it&#039;s greater than what&#039;s on the right. [adding a stick to the greater than sign will turn it into a D].

|&gt; is D for disjunction

also, if you graph the answers on a number line, you can see why it has to be that way.

Answer 4

the second has only two answers, 5 and -5

the first is an inequality so it has a range of answers. between -7 and 7

Answer 5

x^2-49&lt;0

x^2 &lt; 49

|x| &lt; 7

x^2&gt;=25

|x| &gt;=5

we put them together by absolute values