What is the minimum value of $|2x-5|+6$?

Question

michael_b · Answer 1 · 2017-06-09T08:58:37.670

1

With x set as 2.5, the expression would equal 6

Absolute value only returns only floats equal or greater than 0. That being said, the range of this function is:

(0)+6 to (infinity)+6

with the latter being greater obviously because: 6 < Infinity+6

The minimum value would have to make the inside of the function equal 0 which means: $ |2x-5| = 0 $

And since it is zero, we can remove the absolute value sign to get:

$ 2x-5 = 0 $

$ 2x = 5 $

$ x = 2.5 $

Resulting in the expression to be:

$ |2x-5|+6 $

$ |2(2.5)-5|+6 $

$ |5-5|+6 $

$ |0|+6 $

$ = 6 $

EDIT: Accidentally typed former instead of latter.

EDIT: Added Image Proof.

EDIT: Used Expression signs to format instead of quotes.

edited Jun 09 '17 at 08:58

answered Jun 09 '17 at 08:46

michael_b

3

This could be a good answer, if you could format properly! It is easier than you think. Just put every math expression between dollar signs. For example, 2x - 5 = 0 becomes $2x - 5 = 0$ if you put dollar signs around it :) – Jun 09 '17 at 08:50
Thanks! Ill do that, I'm new to SE. :) – michael_b Jun 09 '17 at 08:55
2

Good job! Keep up the good work :) – Jun 09 '17 at 09:10
1

Got it. Thanks alot. – John Jun 09 '17 at 09:20
No Problem John! – michael_b Jun 19 '17 at 02:31

score 0 · Answer 2 · answered Jun 09 '17 at 08:36

0

Hint. The absolute value is non-negative, hence $|2x-5|\geq 0$.

answered Jun 09 '17 at 08:36

Eff

score 0 · Answer 3 · answered Jun 09 '17 at 08:51

0

We have $|2x+5|\geq 0$ for all values of x.

Therefore, $|2x+5|+6 \geq 6$ for all values of $x$.

$|2(-2.5)+5|+6=6$, so this minimum value is achieved at $x=-2.5$.

The minimum of $|2x+5|+6$ is thus $\boxed{6}$.

answered Jun 09 '17 at 08:51

Saketh Malyala