4-|2x-3|<=9
How do I deal with a negative absolute?
2 answers
It's always true? How would I show my work on this
4-|2x-3| ≤ 9
-|2x-3| ≤ 5
|2x-3| ≥ -5
or by default:
|2x-3| ≥ 0 , since the absolute value of anything ≥ 0
2x-3 ≥ 0 OR -2x+3 ≥ 0
x ≥ 3/2
OR
-2x ≥ -3
x ≤ 3/2
so any value of x will work
the solution is the set of real numbers.
look at it this way..
in 4-|2x-3| ≤ 9
the left side has a maximum of 4, which is already ≤ 9
so no matter what we subtract, it can only get smaller, thus it will always be ≤ 9
-|2x-3| ≤ 5
|2x-3| ≥ -5
or by default:
|2x-3| ≥ 0 , since the absolute value of anything ≥ 0
2x-3 ≥ 0 OR -2x+3 ≥ 0
x ≥ 3/2
OR
-2x ≥ -3
x ≤ 3/2
so any value of x will work
the solution is the set of real numbers.
look at it this way..
in 4-|2x-3| ≤ 9
the left side has a maximum of 4, which is already ≤ 9
so no matter what we subtract, it can only get smaller, thus it will always be ≤ 9