Question

For what values of x is the absolute value of x less than or equal to 1.5? (Hint: Substitute numbers into the inequality |x| ≤ 1.5 and see which numbers make the inequality true.) Complete the conjecture about when the absolute value of x is less than or equal to a given positive number k.
The absolute value of x is less than or equal to 1.5 when
(select)
. The absolute value of x is less than or equal to k when
(select)
.

Answer 1

Answer:

|x|<1.5

if x=0

0<1.5 is true

if x=1.5

1.5<1.5

true

if x=-1.5

|-1.5|<1.5

anything greater than 1.5 or less than -1.5 doesn't work

the way to solve is

assume that the inside is negative so if you had

|x|=a then to solve

x=a

x=-a