Question

Decide whether the statement is true or false. If it is​ false, explain why. The union of the solution sets of 4xplus5equals13​, 4xplus5greater than13​, and 4xplus5less than13 is empty set

Answer 1

The given statement is false because it isn't an empty set!

Step-by-step explanation:

We have following sets of inequalities:

$4x+5=13\\4x+5>13\\4x+5<13$

From $4x+5=13$ we get ,

$4x = 8 \\x=2$

Therefore solution set is x=2.

Now, for $4x+5>13$ we get ,  

$4x+5>13 \\4x>8\\x>2$

Therefore solution set is x>2.

For $4x+5<13$ we get ,

$4x+5<13\\4x<8\\x<2$

Therefore solution set is x<2.

Now, the union of x=2, x<2 & x>2 is  -∞<x<∞. i.e. all possible values of x. And so above statement is false because it isn't an empty set!